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UNIVERSITY   OF   CALIFORNIA 


LIBRARY 

OF  THE 

DCPARTMCNT   OF 


Received /..S.../..A..S.. 

Accessions  No .  j£..Pr..7....  Book  No...*b. 


tOWER  W 


PLATE  i 


Beacon  Lith. Co.  Boston 


INTRODUCTION 


TO 


PHYSICAL    SCIENCE. 


BY 


A.  P.  GAGE,  PH.D., 

INSTRUCTOR  IN  PHYSICS,  ENGLISH  HIGH  SCHOOL,  BOSTON,  AND 
AUTHOR  OF  "PRINCIPLES  OF  PHYSICS." 


BOSTON,  ,l7.&A.j:.-  •      -'     . 
GINN   &   COMPANY,   PUBLISHEES. 


Entered  according  to  Act  of  Congress,  in  the  year  1887,  by 

A.  P.  GAGE, 
in  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


TYPOGRAPHY  BY  J.  8.  GUSHING  &  Co.,  BOSTON. 


PRESSWORK  BY  GINN  &  Co.,  BOSTON. 


AUTHOR'S   PREFACE. 


AN  experience  of  about  six  years  in  requiring  individual 
laboratory  work  from  my  pupils  has  constantly  tended  to 
strengthen  my  conviction  that  in  this  way  alone  can  a  pupil 
become  a  master  of  the  subjects  taught.  During  this  time 
I  have  had  the  satisfaction  of  learning  of  the  successful 
adoption  of  laboratory  practice  in  all  parts  of  the  United 
States  and  the  Canadas ;  likewise  its  adoption  by  some  of 
the  leading  universities  as  a  requirement  for  admission.  Mean- 
time my  views  with  reference  to  the  trend  which  should  be 
given  to  laboratory  work  have  undergone  some  modifications. 
The  tendency  has  been  to  some  extent  from  qualitative  to  quan- 
titative work.  With  a  text-book  prepared  on  the  inductive  plan, 
and  with  class-room  instruction  harmonizing  with  it,  the  pupil  will 
scarcely  fail  to  catch  the  spirit  and  methods  of  the  investiga- 
tor, while  much  of  his  limited  time  may  profitably  be  expended 
in  applying  the  principles  thus  acquired  in  making  physical 
measurements. 

A  brief  statement  of  my  method  of  cpnducting  laboratory 
exercises  may  be  of  service  to  some,  until  their  own  experience 
has  taught  them  better  ways.  As  a  rule,  the  principles  and 
laws  are  discussed  in  the  class-room  in  preparation  for  subse- 
quent work  in  the  laboratory.  The  pupil  then  enters  the  labo- 
ratory without  a  text-book,  receives  his  note-book  from  the 
teacher,  goes  at  once  to  any  unoccupied  (numbered)  desk 
containing  apparatus,  reads  on  a  mural  blackboard  the  ques- 
tions to  be  answered,  the  directions  for  the  work  to  be  done 
with  the  apparatus,  measurements  to  be  made,  etc.  Having 
performed  the  necessary  manipulations  and  made  his  observa- 

673277 


iv  AUTHOR'S  PREFACE. 

tions,  he  surrenders  the  apparatus  to  another  who  may  be  ready 
to  use  it,  and  next  occupies  himself  in  writing  up  the  results 
of  his  experiments  in  his  note-book.  These  note-books  are 
deposited  in  a  receptacle  near  the  door  as  he  leaves  the  labo- 
ratory. Nothing  is  ever  written  in  them  except  at  the  times 
of  experimenting.  These  books  are  examined  by  the  teacher  ; 
they  contain  the  only  written  tests  to  which  the  pupil  is  sub- 
jected, except  the  annual  test  given  under  the  direction  of  the 
Board  of  Supervisors.  Pupils,  in  general,  are  permitted  to  com- 
municate with  their  teacher  only.  "  Order,  Heaven's  first 
law,"  is  absolutely  indispensable  to  a  proper  concentration  of 
thought  and  to  successful  work  in  the  laboratory. 

Only  in  exceptional  cases,  such  as  work  on  specific  gravity 
and  electrical  measurements,  has  it  been  found  necessary  to 
duplicate  apparatus.  The  same  apparatus  may  be  kept  on  the 
desks  through  several  exercises,  or  until  every  pupil  has  had 
an  opportunity  of  using  it.  Ordinarily  two  pupils  do  not  per- 
form the  same  kind  of  experiment  at  the  same  time.  With 
proper  system,  any  teacher  will  find  his  labors  lighter  than 
under  the  old  elaborate  lecture  system  ;  and  he  will  never  have 
occasion  to  complain  of  a  lack  of  interest  on  the  part  of  his  pupils. 

I  venture  tc  hope,  in  view  of  the  kind  and  generous  reception 
given  to  the  Elements  of  Physics,  that  this  attempt  to  make 
the  same  methods  available  in  a  somewhat  more  elementary 
work  may  prove  welcome  and  helpful.  It  has  been  my  aim 
in  the  preparation  of  this  book  to  adapt  it  to  the  requirements 
and  facilities  of  the  average  high  school.  With  this  view,  I 
have  endeavored  to  bring  the  subjects  taught  within  the  easy 
comprehension  of  the  ordinary  pupil  of  this  grade,  without 
attempting  to  "popularize"  them  by  the  use  of  loose  and 
unscientific  language  or  fanciful  and  misleading  illustrations 
and  analogies,  which  might  leave  much  to  be  untaught  in  after 
time.  Especially  has  it  been  my  purpose  to  carefully  guard 
against  the  introduction  of  any  teachings  not  in  harmony  with 
the  most  modern  conceptions  of  Physical  Science. 


NOTE    TO    THE    REVISED    EDITION. 


WHILE  the  general  plan  and  arrangement  of  the  original 
edition  of  this  work  have  been  preserved  in  this  revision, 
numerous  changes  dictated  by  experience  and  improved 
methods  of  presenting  portions  of  this  science  have  been 
made  here  and  there  throughout  the  text.  The  subjects  of 
Electricity  and  Magnetism,  however,  have  been  entirely 
rewritten  and  made  to  conform  in  plan  and  arrangement  to 
the  treatment  of  the  same  subjects  in  my  Principles  of 
Physics. 

Although  several  new  topics,  for  instance,  Specific  Heat, 
have  been  introduced,  yet  the  volume  of  the  text  proper  has 
been  increased  only  sixteen  pages.  Aside  from  these  changes 
and  additions,  the  matter  of  the  text  remains  the  same. 

Several  subjects  treated  in  the  text  —  notably  the  Pendu- 
lum, Expansion  Coefficients,  the  Dynamo,  and  the  Electric 
Motor  —  have  been  "continued"  in  the  Appendix  for  the 
benefit  of  those  who  may  wish  to  pursue  these  subjects 
further  than  a  very  elementary  text-book  will  admit. 

I  may  be  permitted  to  suggest  that  copies  of  the  Principles 
of  Physics,  the  style  of  which  is  naturally  similar  to  the  style 
of  this  book,  but  the  treatment  much  fuller,  if  made  accessible 
to  both  teacher  and  pupil,  cannot  fail  to  be  very  helpful  to 
both. 

A.  P.  G. 

1896. 


CONTENTS. 


CHAPTER  I. 

Matter,  energy,  motion,  and  force.  —Attraction  of  gravitation.— 
Molecular  and  molar  forces '.    . 


CHAPTER  II. 

Dynamics  of  fluids.  — Pressure  in  fluids. —Barometers. —Com- 
pressibility and  elasticity  of  gases. —Buoyancy  of  fluids.— 
Density  and  specific  gravity 29 

CHAPTER  III, 

General  dynamics.  —  Momentum,  and  its  relation  to  force.  —  Three 
laws  of  motion. — Composition  and  resolution  of  forces.— 
Center  of  gravity.  —  Falling  bodies.  — Curvilinear  motion.  — 
The  pendulum ; 67 

CHAPTER  IV. 
Work  and  energy.  —  Absolute  system  of  measurements.  —  Ma- 


chines 


CHAPTER  V. 


98 


Molecular  energy,  heat.  —  Sources  of  heat.  —  Temperature. — 
Effects  of  heat.  —  Thermometry.  —Convertibility  of  heat. — 
Thermo-dynamics.  —  Steam-engine 121 


Vlll  CONTENTS. 


CHAPTER  VI. 

PAGE 

Electro-statics.  —  Induction.  —  Potential.  —  Electro-kinetics.  — 
Batteries.  —  Effects  produced  by  electric  current.  —  Elec- 
trical measurements.  —  Resistance  of  conductors.  —  C.G.S. 
magnetic  and  electro-magnetic  units.  —  Galvanometers.  — 
Measuring  resistances.  —  Divided  circuits ;  methods  of 
combining  voltaic  cells.  —  Magnets  and  magnetism.  —  Cur- 
rent and  magnetic  electric  induction.  —  Dynamo-electric  ma- 
chines. —  Electric  light.  —  Electroplating  and  electro  typing. 
—  Telegraphy.  —  Telephony.  —  Thermo-electric  currents  .  .  157 


CHAPTER  VII. 

Sound.  —  Study  of  vibrations  and  waves.  —  Sound-waves,  veloc- 
ity of ;  reflection  of ;  intensity  of ;  re  enforcement  of  ;  inter- 
ference of.  —  Pitch.  —  Vibration  of  strings.  —  Overtones  and 
harmonics.  —  Quality.  —  Composition  of  sonorous  vibrations. 
—  Musical  instruments.  —  Phonograph.  —  Ear 248 


CHAPTER  VIII. 

Radiant  energy,  ether- waves,  light.  —  Photometry.  —  Reflection  of 
light-waves.  —  Refraction.  —  Prisms  and  lenses.  —  Prismatic 
analysis.  —  Color.  —  Thermal  effects  of  radiation.  —  Micro- 
scope and  telescope.  —  Eye.  —  Stereopticon 290 


APPENDIX  :  A,  metric  system  ;  B,  table  of  specific  gravity ;  C, 
table  of  natural  tangents;  D,  simple  pendulum ;  E,  expansion 
coefficients ;  F,  table  of  electrical  resistance ;  G,  dynamos, 
continued ;  H,  electric  motors 357 

INDEX    .  371 


INTRODUCTION  TO  PHYSICAL  SCIENCE. 


Nature  is  the  Art  of  God."  —  THOMAS  BROWNE. 


CHAPTER  I. 
MATTER,   ENERGY,  MOTION,  AND  FORCE. 


Section,  I.. 

»»      »          «  ^  ^    a*     t  3      } 

MATTER  AND  ENERGY.'  " 

To  THE  TEACHER  :  —  That  portion  of  this  book  which  is  printed  in  the 
larger  type,  including  the  experiments,  is  intended  to  constitute  in  itself  a  tolerably 
full  and  complete  working  course  in  Physics.  The  portion  in  fine  print  may, 
therefore,  be  wholly  omitted  without  serious  detriment ;  or  parts  of  it  may 
be  studied  at  discretion  as  time  may  permit ;  or,  perhaps  still  better,  it 
may  be  used  by  the  student,  in  connection  with  works  of  other  authors, 
as  subsidiary  reading.  It  should  be  borne  in  mind  that  recitations  from 
memory  of  mere  descriptive  Physics  and  Chemistry  is  of  little  educational 
value. 

To  THE  PUPIL  :  —  "  Read  nature  in  the  language  of  experiment " ; 
that  is,  put  your  questions,  when  possible,  to  nature  rather  than  to  per- 
sons. Teachers  and  books  may  guide  you  as  to  the  best  methods  of 
procedure,  but  your  own  hands,  eyes,  and  intellect  must  acquire  the 
knowledge  directly  from  nature,  if  you  would  really  know. 

1.  Matter.  —  Physics  is  the  science  that  treats  of  matter 
and  such  changes  in  it  as  do  not  destroy  its  identity.     Any. 
observed   change    in    matter   is    a   phenomenon.     To    the 
question,  What  is  matter?  one  of  the  first  answers  that 
will  occur  to   many  is,    Anything  that  can   be  seen  is 
matter. 

2.  Is  Matter  ever  Invisible  ?  — We  are  usually  able  to 
recognize  matter  by  seeing  it.     We  wish  to  ascertain  by 


MATTER,    ENERGY,    MOTION,    AND   FORCE. 


experiment,  i.e.  by  putting  the  question  to  nature,  whether 
matter  is  ever  invisible.  Now  in  experimenting  there 
must  (1)  be  certain  facts  of  which  we  are  tolerably  certain 
at  the  outset.  These  facts  (2)  lead  us  to  place  things  in 
certain  situations  (the  operation  is  called  manipulation)  in 
order  to  ascertain  what  phenomena  will  follow.  Then,  in 
the  light  of  these  phenomena  we  (3)  reason  from  the  things 
previously  known  to  things  unknown,  i.e.  to  facts  which  we 
wish; to  .ascertain. 

.  For  example,  we  are  certain  that  we  cannot  make  our 
occupy  the  same  space  at  the  same  time.     All 


Fig.  1. 


Fig. 


experience  has  taught  us  that  no  two  portions  of  matter  can 
occupy  the  same  space  at  the  same  time.  This  property 
(called  impenetrability')  of  occupying  space,  and  not  only 
occupying  space,  but  excluding  all  other  portions  of  matter 
from  the  space  which  any  particular  portion  may  chance 
to  occupy,  is  peculiar  to  matter;  nothing  but  matter 
possesses  it.  This  known,  we  have  a  key  to  the  solution 
of  the  question  in  hand. 


MATTER   AND   ENERGY. 

There  is  something  which  we  call  air.  It  is  invisible. 
Is  air  matter?  Is  a  vessel  full  of  it  an  "empty"  vessel 
as  regards  matter  ? 


3. 


Experiment  1.  —  Thrust  one  end  of  a  glass  tube  to  the  bottom  of 
a  basin  of  water;  blow  air  from  the  lungs  through  the  tube,  and 
watch  the  ascending  bubbles.  Do  you  see  the  air  of  the  bubbles,  or 
do  you  see  certain  spaces  from  which  the  air  has  excluded  the  water  ? 


MATTER,  ENERGY,  MOTION,  AND  FORCE. 


Is  air  matter  ?  Is  matter  ever  invisible  ?  State  clearly  the  argument 
by  which  you  arrive  at  the  last  two  conclusions. 

Experiment  2.  —  Float  a  cork  -on  a  surface  of  water,  cover  it  with 
a  tumbler  (Fig.  1)  or  a  tall  glass  jar  (Fig.  2),  and  thrust  the  glass 
vessel,  mouth  downward,  into  the  water.  (In  case  a  tall  jar  is  used, 
the  experiment  may  be  made  more  attractive  by  placing  on  the  cork 
a  lighted  candle.)  State  what  evidence  the  experiment  furnishes 
that  air  is  matter. 

Relying  upon  the  impenetrability  of  air,  men  descend  in  diving-bells 

(Fig.  3)  to  considerable  depths 
in  the  sea  to  explore  its  bot- 
tom, or  to  recover  lost  prop- 
erty. 

Observe  the  cloud  (Fig.  4) 
formed  in  front  of  the  noz- 
zle of  a  boiling  tea-kettle. 
All  the  matter  which  forms 
the  large  cloud  escapes  from 
the  orifice,  yet  it  is  invisible 
at  that  point,  and  only  be- 
comes visible  after  mingling 
with  the  cold  outside  air. 
Place  the  flame  of  an  alcohol 
4«  lamp  in  the  cloud ;  the  matter 

again  becomes  nearly  or  quite  invisible  in  vicinity  of  the  flame.  True 
steam  is  never  visible.  Here  we  see  matter  undergoing  several  changes  from 
the  visible  to  the  invisible  state,  and  vice  versa. 

3.   Matter,  and  only  Matter,  has  Weight.  —  Has  air 

weight  ? 

Experiment  3.  —  Suspend  from  a  scale-beam  a  hollow  globe,  a 
(Fig.  5),  and  place  on  the  other  end  of  the  beam  a  weight,  b  (called  a 
counterpoise),  which  just  balances  the  globe  when  filled  with  air  in 
its  usual  condition.  Then  exhaust  the  air  by  means  of  an  air-pump, 
or  (if  the  scale-beam  is  very  sensitive)  by  suction  with  the  mouth. 
Having  turned  the  stop-cock  to  prevent  the  entrance  of  air,  replace 
the  globe  on  the  beam,  and  determine  whether  the  removal  of  air 
has  occasioned  a  loss  of  weight.  If  air  has  weight,  what  ought  to 


MATTER   AND  ENERGY. 


be  the  effect  on  the  scale-beam  if  you  open  the  stop-cock  and  admit 
air?  Try  it.  Can  matter  exist  in  an  invisible  state?  How  does 
nature  answer  this  question  in  the  last  experiment? 

4.  Energy. — Bodies  of  matter  may  possess  the  ability 
to  put  other  bodies  of  matter  in  motion ;  e.g.  the  bended 
bow  can  project  an  arrow,  and  the  spring  of  a  watch  when 
closely  wound  can  put  in  motion  the  machinery  of  a  watch. 
Ability  to  produce  motion  is  called  energy.  Nothing  but 
matter  possesses  energy.  Does  air  ever  possess  energy? 


Fig.  5. 


Fig.  6. 


Experiment  4.  — Put  about  one  quart  of  water  into  vessel  A 
(Fig.  6),  called  a  condensing-chamber.  Connect  the  condensing- 
syringe  B  with  it,  and  force  a  large  quantity  of  air  into  the  portion 
of  the  chamber  not  occupied  by  water;  in  other  words,  fill  this 
portion  with  condensed  air.  Close  the  stop-cock  C,  and  attach  the 
tube  D  as  in  the  figure.  Open  the  stop-cock,  and  a  continuous  stream 
of  water  will  be  projected  to  a  great  hight. 

Experiment  5.  —  into  the  neck  of  a  flask  (Fig.  7)  partly  filled 
with  water  insert  very  tightly  a  cork  through  which  passes  a  glass 
tube  nearly  to  the  bottom  of  the  flask.  Blow  forcibly  into  the  flask. 
On  removing  the  mouth  the  condensed  air  will  cause  the  water  to 
flow  in  a  stream. 


MATTER,  ENERGY,  MOTION,  AND  FORCE. 


You  will  not  attempt  to  say  what 
matter  is.  This,  no  one  knows.  You 
may,  however,  give  a  provisional  (an- 
swering the  present  needs)  definition  of 
matter,  ix.  draw  the  limiting  line  be- 
tween what  is  matter  and  what  is  not 
matter. 


5.  Minuteness  of  Particles  of  Mat- 
ter. —  If  with  a  knife-blade 
you  scrape  off  from  a  piece 
of  chalk  (not  from  a  black- 
board crayon,  for  this  is  not 
chalk)  a  little  fine  dust,  and 
place  it  under  a  microscope, 
you  will  probably  discover 
Fig.  7.  that  what  seen  with  the  naked 

eye  appear  to  be  extremely  small,  shapeless  particles,  are 
really  clusters  or  heaps  of  shells  and  corals  more  or  less 
broken.  Figure  8 
represents  such  a 
cluster.  Each  of 
these  shells  is  sus- 
ceptible of  being 
broken  into  thou- 
sands of  pieces. 
Reflecting  that 
one  of  these  clus- 
ters is  so  small  as  to  be  nearly  invisible,  you  will  readily 
conceive  that  if  one  of  the  shells  composing  a  cluster 
should  be  broken  into  many  pieces,  and  the  pieces 
separated  from  one  another,  they  would  be  invisible  to 
the  naked  eye.  Yet  the  smallest  of  the  particles  into 


Fig.  8. 


MATTER   AND   ENERGY.  T 

which  one  of  these  shells  can  be  broken  by  pounding  or 
grinding  is  enormously  large  in  comparison  with  bodies 
called  molecules,  which,  of  course,  have  never  been  seen, 
but  in  whose  existence  we  have  the  utmost  confidence. 
(For  definition  and  further  discussion  of  the  molecule,  see 
Chemistry,  page  4.)1 

6.  Theory  of  the  Constitution  of  Matter.  —  For  reasons 
which  will  appear  as  our  knowledge  of  matter  is  extended, 
physicists  have  generally  adopted  the  following  theory  of 
the  constitution  of  matter:  Every  body  of  matter  except  the 
molecule  is  composed  of  exceedingly  small  particles,  called 
molecules.     No    two    molecules    of  matter   in    the   universe 
are  in  permanent  contact  with  each  other.     Every  molecule 
is  in  quivering  motion,  moving  back  and  forth  between  its 
neighbors,   hitting  and  rebounding  from  them.      When  we 
heat  a  body  we  simply  cause  the  molecules  to  move  more 
rapidly  through  their  spaces;    so  they  strike  harder  blows 
on   their   neighbors,  and  usually  push   them  away  a  very 
little  ;  "hence,  the  body  expands. 

7.  Porosity.  —  If  the  molecules  of   a  body  are  never 
in  contact  except  at  the  instants  of  collision,  it  follows 
that  there  are  spaces  between  them.    'These  spaces  are 
called  pores. 

Water  absorbs  air  and  is  itself  absorbed  by  wood,  paper,  cloth,  etc.  It 
enters  the  vacant  spaces,  or  pores,  between  the  molecules  of  these  substances. 
All  matter  is  porous ;  thus  water  may  be  forced  through  the  pores  of  cast 
iron ;  and  gold,  one  of  the  densest  of  substances,  absorbs  liquid  mercury. 

8.  Volume,  Mass,  and  Density.  —  The  quantity  of  space 
a  body  of  matter  occupies  is  its  volume,  and  is  expressed 
in  cubic  inches,  cubic  centimeters,  etc.     By  the  mass  of  a 
body  is  meant  the  quantity  of  matter  in  the  body. 

1  References  in  this  book  are  made  to  the  Introduction  to  Chemical  Science,  by 
B.  P.  Williams. 


8  MATTER,  ENERGY,  MOTION,  AND  FORCE. 

The  unit  of  mass  generally  employed  in  science  is  the 
gram  or  the  pound.  The  gram  is  the  one-thousandth  part 
of  the  standard  kilogram.  This  standard  is  a  piece  of  plati- 
num carefully  preserved  by  the  French  government  at  Paris. 
Originally  it  was  intended  to  represent  the  mass  of  a  cubic 
decimeter  of  pure  water  at  the  temperature  of  4°  C.  A 
kilogram  of  any  substance  is  that  quantity  of  the  substance 
which,  placed  on  a  scale  pan,  would  just  balance  in  a  vacuum 
the  standard  kilogram  placed  on  the  other  pan. 

Experiment  6.  —  Place  on  one  pan  of  a  balance  (Fig.  9)  a  vessel, 
A,  whose  capacity  is  one  liter,  i.e.  one  cubic  decimeter  (see  Appendix). 
Place  upon  the  other  pan  some  body,  B,  which  will  just  counterbalance 
the  empty  vessel.  Then  place  upon  the  same  pan  a  kilogram  mass,  C. 


Fig.  9. 

Now  pour  water  slowly  into  the  vessel  until  the  water  and  kilogram 
mass  counterbalance  each  other.  What  mass  of  water  does  the  vessel 
contain?  How  does  the  mass  of  water  in  A  compare  with  the  mass 
of  the  body  C.?  If  the  weight  of  the  water  in  A  should  change  (its 
mass  remaining  the  same),  should  we  be  able  to  detect  the  change  by 
the  balance? 

Mass  is  quite  distinct  from  weight.  The  weight  of  a  body  is  the 
measure  of  the  attraction  between  it  and  the  earth,  and  is  variable, 
because  the  attraction  of  the  earth  varies  with  the  distance  of  the  body 
from  the  earth,  while  its  mass  remains  constant, 


MATTEK    AND    ENERGY.  9 

The  process  of  measuring  the  mass  of  a  body  must  not  be  con- 
founded with  the  process  of  finding  how  heavy  a  body  is, 
although  both  processes  are,  in  common  usage,  called  weigh- 
ing.    Weighing  a  body  to  ascertain  its  mass  consists  in 
balancing  it  with  a  body  or  bodies  of  known  mass,  and  is 
performed  with  a  scale  balance  and  a  set  of  masses  (com- 
monly called  a  set  of  weights).     Weighing  to   ascertain 
weight  should  be  performed  with  an  instrument  adapted  to 
measuring  force  (§  11),  e.g.  a  spring  balance  (Fig.  10). 
For   most  practical  purposes,  however,  these   instruments         \ 
may  be  used  interchangeably,  inasmuch  as  at  the  same  place        " 
mass  is  proportional  to  weight.1 

Equal  volumes  of  different  substances  (e.g.  cork,  cheese, 
lead)  contain  unequal  quantities  of  matter.  Of  any  two 
substances,  that  which  contains  the  greater  quantity  of 
matter  in  the  same  volume  is  said  to  be  the  denser.  By 
the  density  of  a  body  is  meant  the  mass  of  a  unit  of  volume 
of  the  body.  The  density  of  water  (at  4°  C.)  is  one  gram 
per  cubic  centimeter,  and  the  density. of  cast  iron  is  about 
7.12  grams  per  cubic  centimeter. 

9.  Three  States  of  Matter. — We  recognize  three  states 
or  conditions  of  matter,  viz.,  solid,  liquid  and  gaseous,  fairly 
represented  by  earth,  water  and  air.  Every-day  observa- 
tion teaches  us  that  solids  tend  to  preserve  a  definite  volume 
and  shape  ;  liquids  tend  to  preserve  a  definite  volume  only, 
their  shape  conforms  to  that  of  the  containing  vessel ;  gases 
tend  to  preserve  neither  a  definite  volume  nor  shape,  but  to 
expand  indefinitely.  Liquids  and  gases  in  consequence  of 
their  manifest  tendency  to  flow  are  called  fluids. 

Which  of  the  three  states  any  portion  of  matter  assumes  depends  upon 
its  temperature  and  pressure.  For  example,  at  ordinary  pressure  of  the 

1  This  is  one  of  many  instances  in  physics  in  which  one  quantity  is  indirectly 
measured  by  measuring  another  proportional  to  it. 


10      MATTER,  ENERGY,  MOTION,  AND  FORCE. 

atmosphere  water  is  a  solid  (i.e.  ice),  a  liquid,  or  a  gas  (i.e.  steam),  accord- 
ing to  its  temperature.  In  order  that  matter  may  exist  in  a  liquid  (and 
sometimes  in  a  solid)  state,  a  certain  definite  pressure  is  required.  Ice 
vaporizes,  but  does  not  melt  (i.e.  liquefy)  in  a  space  from  which  the  air 
(and  consequently  atmospheric  pressure)  has  been  removed. 


Section  II. 

RELATIVE  MOTION  AND   RELATIVE  REST. 

1O.  What  constitutes  Relative  Motion  and  Rela- 
tive Rest  ?  —  Motion  is  a  progressive  change  of  position. 
Two  boys  walk  toward  each  other,  or  one  boy  stands, 
and  another  boy  walks  either  toward  or  from  him ; 
in  either  case  there  is  a  relative  motion  between  them, 
because  the  length  of  a  straight  line  (which  may  be  imag- 
ined to  be  stretched)  between  them  constantly  changes. 
One  boy  stands,  and  another  boy  walks  around  him  in  a 
circular  path;  there  is  a  relative  motion  between  them, 
because  the  direction  of  a  straight  line  between  them 
constantly  changes.  There  is  relative  rest  between  two 
boys  while  standing,  because  a  straight  line  between  them 
changes  neither  in  length  nor  direction.  Two  boys  while 
running  are  in  relative  rest  so  long  as  neither  the  distance 
nor  the  direction  from  each  other  changes. 

QUESTIONS. 

1.  What  is  wind?    Give  some  evidence  that  it  possesses  energy. 

2.  Give  a  provisional  definition  of  matter. 

3.  What  is  energy? 

4.  What  is  an  experiment  ?    What  is  manipulation  ? 

5.  What  is  an  air-bubble?    What  important  lesson  does  a  mere 
bubble  teach? 


FORCE.  11 

6.  What  is  impenetrability?     State  several  properties  that   are 
peculiar  to  matter. 

7.  Can  water  be  rendered  invisible  ?    How  ? 

8.  Under  what  conditions  would  a  flock  of  birds  over  your  head  be 
at  rest  with  reference  to  your  body?    Would  the  birds  which  com- 
pose the  flock  be  at  rest  with  reference  to  one  another  ?    An  apple 
rests  upon  a  table ;  are  its  molecules  at  rest  ? 

9.  Why  do  all  moving  bodies  possess  energy?    Do  all  molecules 
possess  energy  ? 

10.  A  span  of  horses  harnessed  abreast  are  drawing  a  street  car  on 
a  straight,  level  road.    Is  there  any  relative  motion  between  the  two 
horses?    Between  the  horses  and  the  carriage?    Between  the  team 
and  objects  by  the  wayside  ?    Suppose  them  to  be  travelling  in  a  cir- 
cular path ;  is  there  relative  motion  between  the  horses  ? 

11.  A  boat  moves  away  from  a  wharf  at  the  rate  of  five  miles  an 
hour.     A  person  on  the  boat's  deck  walks  from  the  prow  toward  the 
stern,  at  the  rate  of  four  miles  an  hour;  what  is  his  rate  of  motion,  i.e. 
his  velocity,  with  reference  to  the  wharf?    What  is  his  velocity  with 
reference  to  the  boat? 

12.  When  is  there  relative  motion  between  two  bodies  ? 


Section  III. 

FORCE. 

11.  Pushes  and  Pulls.  —  We  are  familiar  with  the 
results  of  muscular  force  in  producing  motion.  We  are 
also  aware  that  there  are  forces,  or  causes  of  motion,  quite 
independent  of  man ;  e.g.,  the  force  exerted  by  wind, 
running  water,  and  steam.  If  we  observe  carefully,  we 
shall  find  that  all  motions  are  produced  by  pushes  or  pulls. 
It  is  evident  that  there  can  be  no  push  or  pull  except  be- 
tween at  least  two  bodies  or  two  parts  of  the  same  body. 


12       MATTER,  ENERGY,  MOTION,  AND  FORCE. 

Commonly,  the  bodies  between  which  there  is  a  push  or 
a  pull  are  either  in  contact,  as  when  we  push  or  pull  a 
table,  or  the  action  is  accomplished  through  an  intermedi- 
ate body,  as  when  we  draw  some  object  toward  us  by 
means  of  a  string,  or  push  an  object  away  with  a  pole. 
Can  two  bodies  push  or  pull  without  contact  and  without 
any  tangible  intermediate  body ;  i.e.  is  there  ever  "action 
at  a  distance  "  ? 

Experiment  7.  —  Fill  a  large  bowl  or  pail  with  water  to  the  brim. 
Place  on  the  surface  of  the  water  a  half-dozen  (or  more)  floating  mag- 
nets (pieces  of  magnetized  sewing-needles  thrust  through  thin  slices 
of  cork).  Hold  a  bar  magnet  vertically  over  the  water  with  one  end 
near,  but  not  touching,  the  floats ;  the  floats  either  move  toward  or 
away  from  the  magnet.  Invert  the  magnet,  and  the  motions  of  the 
floats  will  be  reversed. 

Notwithstanding  there  is  no  contact  or  visible  connection  between 
the  floats  and  the  magnet,  the  motions  furnish 
conclusive  evidence  that  there  are  pushes  and 
pulls.  The  motions  are  said  to  be  due  to  mag- 
netic force. 

Experiment  8.  —  Suspend  two  pith  balls  by 
silk  threads.  Rub  a  large  stick  of  sealing-wax 
with  a  dry  flannel,  and  hold  it  near  the  balls. 
The  balls  move  to  the  wax  as  if  pulled  by  it, 
and  remain  in  contact  with  it  for  a  time.  Soon 
they  move  away  from  the  wax  as  if  pushed  away. 
Remove  the  wax;  the  balls  do  not  hang  side 
Fig.  11.  by  side  as  at  first,  but  push  each  other  apart 

(Fig.  11).    These  motions  are  said  to  be  due  to  electric  force. 

12.  How  Force  is  Measured. — Pulling  and  pushing 
forces  may  be  strong  or  weak,  and  are  capable  of  being 
measured.  The  common  spring  balance  (Fig.  12)  is  a 
very  convenient  instrument  for  measuring  a  pulling  force. 
As  usually  constructed,  the  spring  balance  contains  a  spiral 
coil  of  wire,  which  is  elongated  by  a  pull;  and  the  pulling 


FORCE.  13 

force  is  measured  by  the  extent  of  the  elongation. 
may    be    so    constructed    that    an    elongated       A 
coil  may  be  compressed  by  a  pushing  force; 
and  when  so  constructed  it  serves  to  measure 
a  pushing  force  by  the  degree  of  compression. 
All  instruments  that   measure   force,  however 
constructed,  are   called    dynamometers    (force- 
measures).     Observe  that  force  is  measured  in 
pounds ;  in  other  words,  the  unit  by  which  force 
is  measured  is  called  a  pound. 

13.    Equilibrium  of  Forces. 

Experiment  9.  —  Take  a  block  of  wood ;  insert  two  stout  screw- 
eyes  in  opposite  extremities  of  the  block.  Attach  a  spring  balance  to 
each  eye.  Let  two  persons  pull  on  the  spring  balances  at  the  same 
time,  and  with  equal  force,  as  shown  by  their  indexes,  but  in  opposite 
directions.  The  block  does  not  move.  One  force  just  neutralizes  the 
other,  and  the  result,  so  far  as  the  movement  of  the  block,  i.e.  the  body 
acted  on,  is  concerned,  is  the  same  as  if  no  force  acted  on  it.  When 
one  action,  i.e.  one  push  or  pull,  opposes  in  any  degree  another 
action,  each  is  spoken  of  as  a  resistance  to  the  other.  Let  f  represent 
the  number  of  pounds  of  any  given  force,  and  let  a  force  acting  in 
any  given  direction  be  called  positive,  and  indicated  by  the  plus  (+) 
sign,  and  a  force  when  acting  in  an  opposite  direction  to  a  force 
which  we  have  denominated  positive,  be  called  negative,  and  indicated 
by  the  minus  (— )  sign.  Then  if  two  forces  +/and  —/acting  on  a 
body  at  the  same  point  or  along  the  same  line  are  equal,  the  result  is 
that  no  change  of  motion  is  produced. 

Viewed  algebraically,  +/— /=  0 ;  or,  correctly  interpreted,  +/— /— 
(is  equivalent  to)  0,  i.e.  no  force.  In  all  such  cases  there  is  said  to 
be  an  equilibrium  of  forces,  and  the  body  is  said  to  be  in  a  state  of  equi- 
librium. If,  however,  one  of  the  forces  is  greater  than  the  other,  the 
excess  is  spoken  of  as  an  unbalanced  force,  and  its  direction  is  indi- 
cated by  one  or  the  other  sign,  as  the  case  may  be.  Thus,  if  a  force 
of  +  8  pounds  act  on  a  body  toward  the  east,  and  a  force  of  —  10  pounds 
act  on  the  same  body  along  the  same  line  toward  the  west,  then  the 
unbalanced  force  is  —2  pounds,  i.e.  the  result  is  the  same  as  if  a 
force  of  only  2  pounds  acted  on  the  body  toward  the  west. 


14  MATTER,    ENERGY,    MOTION,    AND   FORCE. 

14.    Stress,  Action,  and  Keaction ;  Force  Defined.  — 

An  unbalanced  force  always  produces  a  change  of  motion. 
As  there  are  always  two  bodies  or  two  parts  of  a  body  con- 
cerned in  every  push  or  pull,  there  must  be  two  bodies  or 
parts  of  a  body  affected  by  every  push  or  pull.  When  the 
effects  on  both  parties  to  an  action  are  considered  with- 
out special  reference  to  either  alone,  the  force  is  fre-. 
quently  called  a  stress.1  But  when  we  consider  the  effect 
on  only  one  of  two  bodies,  we  find  it  convenient,  and 
almost  a  necessity,  to  speak  of  the  effect  as  due  to  the 
action  of  some  other  body,  or,  still  more  conveniently,  to  an 
external  force.  The  body  which  acts  upon  another,  itself 
experiences  the  effect  of  the  reaction  of  the  same  force. 

To  increase  or  decrease  the  speed  of  a  moving  body, 
or  to  change  the  direction  of  its  motion,  requires  an  un- 
balanced force.  Force  may  be  provisionally  denned  as  the 
immediate  cause  that  produces,  or  tends  to  produce,  a  change 
of  motion  either  in  magnitude  or  direction.  This  definition 
conveys  no  idea  of  what  force  is ;  it  merely  distinguishes 
between  what  is  force  and  what  is  not  force. 

QUESTIONS. 

1.  Give  a  provisional  definition  of  force.     In  what  two  ways  is  it 
exerted  ? 

2.  How  is  motion  produced ?     Destroyed?     Changed  in  any  way  ? 

3.  How  many  bodies  or  parts  of  a  body  must  be  concerned  in  the 
action  of  any  single  force  ?     How  many  are  affected  thereby  ? 

4.  What  effect  does  an  unbalanced  force  produce  on  a  body  ? 

5.  How  must  the  magnitude  of  two  forces  compare,  and  in  what 
directions  must  they  act  with  reference  to  each  other,  that  they  may 
be  in  equilibrium? 

6.  When  is  a  body  in  equilibrium  ? 

7.  In  what  units  is  force  estimated  ?      In  what  units  is  mass 
estimated?     What  force  is  required  to  support  10  pounds  of  sugar? 

1  Tension  in  a  stretched  rubber  band,  and  pressure  between  two  bodies  in  contact 
when  compressed,  are  illustrations  of  stress. 


ATTRACTION  OF   GRAVITATION.  15 

8.  Why  will  not  a  force  of  10  pounds  raise  10  pounds  of  sugar  ? 
If  the  force  produces  no  change  of  motion,  how  can  it  consistently  be 
called  a  force  ? 

9.  A  bullet  is  flying  unimpeded  through   space;  does  it  possess 
energy?     Is  it  (disregarding  the  force  of  gravity)  exerting  force? 
Would  it  exert  force  if  it  should  encounter  some  other  body?    Which 
produces  motion,  energy  or  force  ?    Which  denotes  ability  to  produce 
motion  ? 


Section  IV. 

ATTRACTION   OF   GRAVITATION. 

15.  Gravitation  is  Universal.  —  An  unsupported  body 
falls  to  the  earth.     This  is  evidence  of  an  action  or  stress 
between  the  earth  and  the  body.     It  has  been  ascertained 
by  careful  observation  that  when  a  ball  is  suspended  by 
a  long  string  by  the  side  of  a  mountain,  the  string  is 
not  quite  vertical,  but  is  deflected  toward  the  mountain  in 
consequence  of  an  attraction  between  the  mountain  and 
the   ball.     That  there  is  an  attraction  between  the  sun 
and  the  earth,  and  the  earth  and  the  moon,   is  shown,  as 
we  shall   see   further   on,   by   their   curvilinear   motions. 
Tides  and  tidal  currents  on   the   earth   are   due  to  the 
attraction  of  the  sun  and  the  moon. 

This  attraction  is  called  gravitation.  When  bodies  under 
its  influence  tend  to  approach  one  another,  they  are  said 
to  gravitate.  Since  this  attraction  ever  exists  between  all 
bodies,  at  all  distances,  it  is  called  universal  gravitation. 

16.  Law   of  Universal    Gravitation.  —  Methods    too 
difficult  for   us   to    comprehend    at    present    have    estab- 


16  MATTER,    ENERGY,    MOTION,    AND   FORCE. 

lished  the  fact  that  the  strength  of  the  attraction  between 
any  two  bodies  depends  upon  two  things;  viz.,  their 
masses,  and  the  distance  between  certain  points  within 
the  bodies  (to  be  explained  hereafter),  called  their  cen- 
ters of  gravity.  The  following  law  is  found  everywhere 
to  exist  :  — 

The  attraction  between  every  two  bodies  of  matter  in  the 
universe  varies  directly  as  the  product  of  their  masses,  and 
inversely  as  the  square  of  the  distance  between  their  centers 
of  gravity.  Representing  the  masses  of  two  bodies  by 
m  and  m',  the  distance  by  d,  and  the  attraction  by  g, 
this  relation  is  expressed  mathematically,  thus  :  g  <x 


(varies  as)  ^m~.     For  example,  if  the  mass  of  either  body 

is  doubled,  the  product  (mm')  of  the  masses  is  doubled, 
and  consequently  the  attraction  is  doubled.  If  the  dis- 
tance between  their  centers  of  gravity  is  doubled,  then 

(—  =  -)  the  attraction  becomes  one-fourth  as  great. 

The  mass  of  the  moon  is  very  much  less  than  that  of  the  earth  ;  hence 
the  force  of  gravity  at  the  surface  of  the  former  is  much  less  than  at  the 
surface  of  the  latter.  A  person  who  could  leap  a  fence  three  feet  high  on 
the  earth,  could,  by  the  exertion  of  the  same  muscular  energy,  leap  a  fence 
18  feet  high  on  the  moon.  A  boy  might  throw  a  stone  a  greater  distance 
on  the  moon  than  a  rifle  can  project  a  bullet  on  the  earth.  The  masses  of 
Jupiter  and  Saturn,  being  so  much  greater  than  that  of  the  earth,  the 
corresponding  greater  attraction  which  they  would  exert  would  so  impede 
locomotion  that  a  person  would  be  able  ojily  to  crawl  along  as  though  his 
feet  were  weighted  with  lead. 

1  7.  Weight.  —  The  weight  of  a  body  is  the  measure  of 
the  attraction  between  it  and  the  earth.  It  is  applied  only 
to  terrestrial  bodies.  We  say  that  the  weight  of  a  certain 
body  is  ten  pounds,  meaning  that  this  is  the  measure  of 
the  force  of  attraction  between  this  body  and  the  earth. 


ATTRACTION  OF  GRAVITATION.  17 

From  the  law  of  gravitation  we  infer  that  at  equal  dis- 
tances from  the  earth's  center  of  gravity  the  weight  of 
bodies  varies  as  their  masses.  Hence,  when  we  weigh  a  body 
we  measure  at  the  same  time  both  the  force  with  which 
the  earth  attracts  it  and  its  mass  ;  and  both  quantities 
are  commonly  expressed  in  units  of  the  same  name.  The 
expression  four  pounds  of  tea  conveys  the  twofold  idea 
that  the  quantity  of  tea  is  four  pounds,  and  that  the  force 
with  which  the  earth  attracts  the  tea  is  four  pounds. 

Again,  we  infer  from  the  law  of  gravitation  (1)  that 
a  body  iveighs  more  at  a  given  point  on  the  surface  of  the 
earth  than  at  any  point  above  this  point. 

(2)  That  inasmuch  as  some  points  on  the  earth's  sur- 
face are  nearer  its  center  of  gravity  than  others,  the  same 
body  will  not  have  the  same  weight  at  all  points  on  the  earths 
surface.  A  given  body  stretches  a  spring  balance  less  as 
it  is  carried  from  either  pole  toward  the  equator.  The 
loss  of  weight  due  to  the  increase  of  distance  from  the 
center  of  the  earth  is  -g-^g-  of  its  weight  at  the  poles. 


18.  Gravitation  Units  of  Force.  —  The  weight  of  a 
body  is  found  by  determining  the  elongation  of  the  spring 
in  the  spring-balance  (§  12).  The  units  employed  are  the 
pound  and  the  kilogram,  and  are  called  the  gravitation 
units1  of  force.  All  forces  may  be  measured  in  the  same 
units.  To  say  that  a  man  pulls  a  boat  with  a  force  of  one 
hundred  pounds  is  equivalent  to  saying  that  he  pulls  with 
a  force  equal  to  the  force  which,  at  that  locality,  acts 
between  the  earth  and  a  body  having  a  mass  of  one 

1  There  are  two  sytems  of  units  in  use,  the  Gravitation  System  and  the  Absolute 
System.  In  the  former  the  pound  or  kilogram  denotes  force  or  mass,  in  the  latter 
they  denote  only  mass. 


18  MATTER,    ENERGY,    MOTION,    AND   FORCE. 

hundred  pounds.  A  force  of  one  pound,  then,  is  an 
abbreviated  expression  for  a  force  equal  to  the  weight 
(at  the  locality  in  question)  of  one  pound  of  matter. 

QUESTIONS. 

1.  If  the   earth's   mass   were   doubled   without   any  change   of 
volume,  how  would  it  affect  your  weight? 

2.  On  what  principle  do  you  determine  that  the  mass  of  one  body 
is  ten  times  the  mass  of  another  body? 

3.  How  many  times  must  you  increase  the  distance  between  the 
centers  of  two  bodies  that  their  attraction  may  become  one-fourth  ? 

4.  If  a  body  on  the  surface  of  the  earth  is  4,000  miles  from  the 
center  of  gravity  of  the  earth,  and  weighs  at  this  place  100  pounds, 
what  would  the  same  body  weigh  if  it  were  taken  4,000  miles  above 
the  earth's  surface  ? 


Section  V. 

MOLECULAR   FORCES. 

19.  Molecular  Attractive  Forces ;  Molecular  Dis- 
tinguished from  Molar  Forces.  —  Thus  far  we  have 
considered  only  the  effects  of  the  action  of  bodies  of 
sensible  (perceived  by  the  senses)  size  and  at  sensible 
distances.  Have  we  any  evidence  that  the  molecules 
which  compose  these  bodies  act  upon  one  another  in  a 
similar  manner? 

If  you  attempt  to  break  a  rod  of  wood  or  iron,  or  stretch 
a  piece  of  rubber,  you  realize  that  there  is  a  force  resisting 
you.  You  reason  that  if  the  supposition  be  true,  that  the 
grains  or  molecules  that  compose  these  bodies  do  not 


MOLECULAR   FORCES.  19 

touch  one  another,  then  there  must  be  a  powerful  attrac- 
tive force  between  the  molecules,  to  prevent  their  separa- 
tion. After  stretching  the  rubber,  let  go  one  end  ;  it 
springs  back  to  its  original  form.  What  is  the  cause  ? 

Every  body  of  matter,  whether  solid,  liquid,  or  gaseous, 
may  be  forced  into  a  smaller  volume  by  pressure  ;  in 
other  words,  matter  is  compressible.  When  pressure  is 
removed,  the  body  expands  into  nearly  or  quite  its 
original  volume.  What  is  the  cause  ?  According  to  the 
theory  of  the  constitution  of  matter  (§  6)  the  molecules 
of  every  mass  are  in  ceaseless  motion,  hitting  and  re- 
bounding from  one  another.  This  tends  to  drive  the 
molecules  apart.  In  gaseous  masses  the  molecules  move 
without  restraint ;  hence  gaseous  bodies  always  tend  to 
expand.  In  solids  and  liquids  the  molecules  are  held 
under  the  action  of  a  very  powerful  attractive  force  which 
prevents  their  separation  beyond  certain  limited  distances 
except  under  the  action  of  considerable  external  force. 
If,  however,  the  molecular  motions  in  solid  and  liquid 
masses  become  great  enough  (i.e.  the  masses  be  sufficiently 
heated)  the  molecules  will  become  separated  beyond  the 
limits  of  this  attractive  force,  and  the  solids  and  liquids 
will  be  converted  into  gases. 

For  convenience,  we  call  bodies  of  appreciable  size 
molar  (massive)  in  distinction  from  molecules  (bodies  of 
very  small  mass).  Action  between  molar  bodies,  usually 
at  sensible  distances,  is  called  molar  force  ;  action  between 
molecules,  always  at  insensible  distances,  is  called  molec- 
ular force. 

2O.  Cohesion,  Tenacity.  —  That  attraction  which  holds 
the  molecules  of  solids  and  liquids  together,  so  as  to  form 


20  MATTER,    ENERGY,    MOTION,    AND   FORCE. 

masses,  is  called  cohesion.  It  is  the  attraction  that  resists 
a  force  tending  to  break  or  crush  a  body.  The  tenacity 
of  solids  and  liquids,  i.e.  the  resistance  which  they  offer  to 
being  pulled  apart,  is  due  to  this  attraction.  It  is  greatest 
in  solids,  usually  less  in  liquids,  and  entirely  wanting  in 
gases.  It  acts  only  at  insensible  distances,  and  is  strictly 
molecular.  When  cohesion  is  overcome,  it  is  usually  diffi- 
cult to  force  the  molecules  near  enough  to  one  another  for 
this  attraction  to  become  effective  again.  Broken  pieces 
of  glass  and  crockery  cannot  be  so  nicely  readjusted  that 
they  will  hold  together.  Yet  two  polished  surfaces  of 
glass  or  metal,  placed  in  contact,  will  cohere  quite  strongly. 
Or  if  the  glass  is  heated  till  it  is  soft,  or  in  a  semi-fluid 
condition,  then,  by  pressure,  the  molecules  at  the  two 
surfaces  will  flow  around  one  another,  pack  themselves 
closely  together,  and  the  two  bodies  will  become  firmly 
united.  This  process  is  called  welding.  In  this  manner 
iron  is  welded. 

Cohesive  force  varies  greatly  both  in  intensity  and  its  behavior  in  differ- 
ent substances,  and  even  in  the  same  substances  under  different  circum- 
stances. Modifications  of  this  force  give  rise  to  certain  conditions  of  matter 
designated  as  crystalline  or  amorphous,  hard  or  soft,  flexible  or  rigid,  elastic, 
viscous,  malleable,  ductile,  tenacious,  etc. 

21.   Crystallization. 

Experiment  10.  —  Pulverize  about  three 
ounces  of  alum.  Take  about  a  teacupful  of 
boiling  hot  water  in  a  beaker,  and  sift  into  it 
the  powdered  alum,  stirring  with  a  glass  rod 
as  long  as  the  alum  will  dissolve  readily. 
Then  suspend  in  the  liquid  to  a  little  depth 
one  or  more  threads  from  a  splinter  of  wood 
Fig  13  laid  across  the  top  of  a  beaker  (Fig.  13). 

Place  the  whole  where  it  will  not  be  disturbed, 

and  allow  it  to  cool  slowly.     It  is  well  to  allow  it  to  stand  for  a  day  or 

more. 


MOLECULAR   FORCES. 


21 


Beautiful  transparent  bodies  of  regular  shape  are  formed 
on  the  bottom  and  sides  of  the  beaker  and  probably  on 
the  thread.  They  are  called  crystals,  and  the  process  by 
which  they  are  formed  is  called  crystallization. 

Observe  that  the  crystals  formed  on  the  thread  in  mid- 
liquid  are  much  more  regular  in  shape  than  those  formed 
on  the  surface  of  the  glass.  The  latter  are  flattened,  and 
are  said  to  be  tabular. 

In  a  similar  manner,  obtain  crystals  of  bichromate  of  potash,  blue  vitriol, 
copperas,  etc.  Make  up  a  cabinet  of  crystals,  preserving  them  in  small, 
closely  stoppered  glass  bottles. 

Experiment  11.  —  Thoroughly  clean  a  piece  of  window  glass,  by 
breathing  upon  it,  and  then  rubbing  it  with  a  piece  of  newspaper. 


Fig.  14. 

Warm  the  glass  over  an  alcohol  or  Bunsen  flame,  and  pour  upon  the 
glass  a  strong  solution  of  sal  ammoniac,  or  saltpetre.  Allow  the 
liquid  to  drain  off,  and  hold  the  wet  glass  up  to  the  sunlight,  or  view 
it  through  a  magnifying  glass,  and  watch  the  growth  of  the  crystals. 

Experiment  12.  —  Examine  with  a  magnifying  glass  the  surface 
'fracture  of  a  freshly  broken  piece  of  sugar  loaf,  and  observe,  if  any, 
small,  smooth,  glistening  planes  thus  exposed. 

These  planes  are  surfaces  of  small,  imperfectly  formed 
crystals  closely  packed  together,  similar  to  the  imperfect 


22  MATTER,   ENERGY,   MOTION,   AND   FORCE. 

crystals  of  alum,  etc.,  formed  on  the  sides  of  the  beaker. 
Such  bodies  are  said  to  have  a  crystalline  fracture ',  and  the 
body  itself  is  said  to  be  crystalline  in  distinction  from 
amorphous  matter  like  glass,  glue,  etc.,  which  furnish  no 
evidence  of  crystalline  structure. 

Very  interesting  illustrations  of  crystallization  are  those  delicate  lace- 
like  figures  which  follow  the  touch  of  frost  on  the  window-pane.  Figure 
14  represents  a  few  of  more  than  a  thousand  forms  of  snowflakes  that  have 
been  discovered,  resulting  from  a  variety  of  arrangement  of  the  water 
molecules. 

Snow  crystals  are  formed  during  free  suspension  of  moisture  in  the  air 
and  without  interference  from  contact  with  any  solid;  hence  their  per- 
fection of  growth.  If  you  gather  snowflakes,  as  they  fall,  on  cold,  yellow 
glass  and  examine  them  under  a  magnifying  glass,  you  will  find  that  all 
crystals  have  a  primary  type  of  six  rays,  and  hexagonal  outline.  Professor 
Tyndall  has  succeeded  in  so  unravelling  lake  ice  as  to  show  what  he  calls 
"  liquid  flowers  "  in  a  block  of  ice,  thus  proving  that  ice  is  crystalline,  or 
composed  of  a  compact  mass  of  crystals.  (Read  Tyndall's  "Forms  of 
Water.") 

Nature  teems  with  crystals.  Nearly  every  kind  of  matter,  in  passing 
from  the  liquid  state  (whether  molten  or  in  solution)  to  the  solid  state, 
tends  to  assume  symmetrical  forms.  Crystallization  is  the  rule  ;  amorphism, 
the  exception.  You  can  scarcely  pick  up  a  stone  and  break  it  without  find- 
ing the  same  crystalline  fracture. 

The  massive  pillars  of  basaltic  rock  found  in  certain  localities,  for  ex- 
ample, in  Fingal's  Cave  (Fig.  15),  might  in  its  broadest  sense  be  regarded 
as  forms  of  crystallization,  inasmuch  as  they  are  the  result  of  natural 
causes.  These  hexagonal  columns,  however,  probably  resulted  from  great 
lateral  pressure,  exerted  while  cooling,  upon  molten  matter  thrown  up 
ages  ago  by  submarine  volcanoes. 

This  tendency  of  the  molecules  of  matter  to  arrange  themselves  in 
definite  ways  during  solidification  is  attended  usually  with  a  change  of 
volume.  The  molecular  force  exerted  at  such  a  time  is  sometimes  enor- 
mous, so  as  to  burst  the  strongest  vessels.  Hence  our  service  pipes  are 
burst  when  water  is  allowed  to  crystallize  (freeze)  in  them. 

22.  Hardness. 

Experiment  13.  —  Get  specimens  of  the  following  substances:  talc, 
chalk,  glass,  quartz,  iron,  silver,  lead,  copper,  rock-salt,  and  marble. 
Ascertain  which  of  them  will  scratch  glass,  and  which  are  scratched 


MOLECULAR   FORCES. 


23 


by  glass.  Which  is  the  softest  metal  that  you  have  tried  ?  The  hard- 
est ?  Name  some  metal  that  you  can  scratch  with  a  finger-nail.  See 
if  you  can  scratch  a  piece  of  copper  with  a  piece  of  lead,  and  vice  versa. 
Which  is  softer,  iron  or  lead?  Which  is  the  denser  metal?  Does 
hardness  depend  upon  density?  What  force  must  be  overcome  in 
order  to  scratch  a  substance  ? 


ITig.  15. 

To  enable  us  to  express  degrees  of  hardness,  the  following  table  of 
reference  is  generally  adopted :  — 


MOHR  S    SCALE    OF    HARDNESS. 

6.  Orthoclase  (Feldspar). 

7.  Quartz. 

8.  Topaz. 

9.  Corundum. 
10.  Diamond. 


1.  Talc. 

2.  Gypsum  (or  Rock-Salt). 

3.  Calcite. 

4.  Fluor-Spar. 

5.  Apatite. 

By  comparing  a  given  substance  with  the  substances  in  the  table,  its 
degree  of  hardness  can  be  expressed  approximately  by  one  of  the  numbers 
used  in  the  table.  If  the  hardness  of  a  substance  is  indicated  by  the  num- 
ber 4,  what  would  you  understand  by  it  ? 

23.   Hardening  and  Annealing ;   Flexibility. 

Experiment  14.  —  Get  pieces  of  wire,  each  ten  inches  long,  of  the 
following  metals :  steel,  iron,  spring  brass,  hard  copper,  German  silver, 


24  MATTER,   ENERGY,   MOTION,   AND  FORCE. 

platina,  and  phosphor-bronze.  Place  each  in  an  alcohol  or  Bunsen 
flame,  and  heat  the  wire  near  one  end  to  a  bright  red  glow,  and  then 
thrust  the  heated  part  into  cold  water,  and  suddenly  cool  it.  See 
whether  the  part  thus  treated  bends  more  or  less  readily  than  the 
part  which  has  not  suffered  the  sudden  change.  When  a  body  is 
easily  bent,  i.e.  its  cohesive  force  admits  of  a  hinge-like  movement 
among  its  molecules  without  permanent  separation,  it  is  said  to  be 
flexible.  See  whether  the  part  treated  has  been  hardened  or  softened 
by  the  treatment.  The  process  of  rendering  flexible  and  softening  is 
called  annealing. 

Next  heat  the  opposite  ends  of  the  wires  as  before,  and  slowly  (10 
to  15  minutes)  withdraw  the  wires  from  the  flame  by  gradually 
raising  them  above  the  flame,  in  order  that  the  fall  of  temperature  may 
be  very  gradual.  Ascertain  as  before  the  effect  of  this  treatment  on 
the  flexibility  and  hardness  of  each.  Classify  the  substances  as  an- 
nealed by  sudden  cooling,  and  annealed  by  slow  cooling. 

24.  Elasticity. 

Experiment  15. —  Obtain  thin  strips  of  as  many  of  the  following 
substances  as  practicable :  rubber,  different  kinds  of  wood,  ivory, 
whalebone,  steel,  spring  brass  and  soft  brass,  copper,  iron,  zinc,  and 
lead. 

Bend  each  one  of  the  above  strips.  Note  which  completely  unbends 
when  the  force  is  removed.  Arrange  the  names  of  these  substances  in 
the  order  of  the  rapidity  and  completeness  with  which  they  unbend. 

The  property  which  matter  possesses  of  recovering  its  former  form 
or  volume,1  after  having  yielded  to  some  force,  is  called  elasticity. 

25.  Viscosity. 

Experiment  16.  —  Support  in  a  horizontal  position,  at  one  of  its 
extremities,  a  stick  of  sealing-wax,  and  suspend  from  its  free  extrem- 
ity an  ounce  weight,  and  let  it  remain  in  this  condition  several  days, 
or  perhaps  weeks.  At  the  end  of  the  time  the  stick  will  be  found 
permanently  bent.  Had  an  attempt  been  made  to  bend  the  stick 
quickly,  it  would  have  been  found  quite  brittle.  A  body  which, 
subjected  to  a  stress  for  a  considerable  time,  suffers  a  permanent 
change  in  form  is  said  to  be  viscous. 

1  It  is  called  elasticity  of  form  when  the  form  is  restored  after  removing  the 
distorting  force,  and  elasticity  of  volume  when  the  original  volume  is  restored. 
Fluids  possess  only  elasticity  of  volume. 


MOLECULAR   FORCES.  25 

Sealing-wax  and  pitch  may  be  regarded  as  fluids  whose  flow  is  ex- 
tremely slow ;  i.e.  their  viscosity  or  resistance  to  flow  is  very  great. 
Liquids  like  molasses  and  honey  are  said  to  be  viscous,  in  distinc- 
tion from  limpid  liquids  like  water  and  alcohol. 

26.  Malleability  and  Ductility. 

Experiment  17:  —  Place  a  piece  of  lead  on  an  anvil,  or  other  flat 
bar  of  surface,  and  hammer  it.  It  spreads  out  under  the  hammer  into 
sheets,  without  being  broken,  though  it  is  evident  that  the  molecules 
have  moved  around  one  another,  and  assumed  entirely  different 
relative  positions.  Heat  a  piece  of  soft  glass  tube  in  a  gas-flame,  and, 
although  the  glass  does  not  become  a  liquid,  it  behaves  very  much  like 
a  liquid,  and  can  be  drawn  out  into  very  fine  threads. 

When  a  solid  possesses  sufficient  fluidity  to  admit  of  being  drawn 
out  into  threads,  it  is  said  to  be  ductile.  When  it  will  admit  of  being 
hammered  or  rolled  into  sheets,  it  is  said  to  be  malleable. 

Platinum  and  gold  are  the  most  malleable  and  ductile  metals.  They 
can  be  drawn  into  wire  finer  than  a  spider's  thread,  or  so  as  to  require 
very  keen  vision  to  see  it.  Gold  can  be  hammered  into  leaves  sWozrtf  °^ 
an  inch  thick.  Some  metals,  like  iron,  are  more  malleable  and  ductile  at 
a  red  heat ;  others,  like  copper,  at  an  ordinary  temperature. 

It  is  remarkable  that  the  tenacity  of  most  metals  is  increased  by  being 
drawn  out  into  wires.  It  would  seem  that,  in  the  new  arrangement  which 
the  molecules  assume,  the  cohesive  force  is  stronger  than  in  the  old. 
Hence  cables  made  of  iron  wire  twisted  together,  so  as  to  form  an  iron 
rope,  are  stronger  than  iron  chains  of  equal  weight  and  length,  and  are 
much  used  instead  of  chains  where  great  strength  is  required. 

27.  Adhesion.  —  If  you  touch  with  your  finger  a  piece 
of  gold-leaf,  it  will  stick  to  your  finger ;  it  will  not  drop 
off,  it  cannot  be  shaken  off;  and  an  attempt  to  pull  it  off 
increases  the  difficulty.     Dust  and  dirt  stick  to  clothing. 
Thrust  your  hand  into  water,  and  it  comes  out  wet.     We 
could   not   pick   up  anything,  or   hold   anything   in   our 
hands,  were  it  not  that  these  things  stick  to  the  hands. 

Every  minute's  experience  teaches  us  that  not  only  is 
there  an  attractive  force  between  molecules  of  the  same 


26  MATTER,    ENERGY,    MOTION,    AND   FORCE. 

kind  of  matter,  but  there  is  also  an  attractive  force 
between  molecules  of  unlike  matter.  That  force  which 
causes  unlike  substances  to  cling  together  is  called  ad- 
hesion.^ It  is  probable  that  there  is  some  adhesion  between 
all  substances  when  brought  in  contact.  Glass  is  wet  by 
water,  but  is  not  wet  by  mercury.  If  a  liquid  adheres  to 
a  solid  more  firmly  than  the  molecules  of  the  liquid  cohere, 
then  will  the  solid  be  wet  by  the  liquid.  If  a  solid  is  not 
wet  by  a  liquid,  it  is  not  because  adhesion  is  wanting,  but 
because  cohesion  in  the  liquid  is  stronger. 

28.  Tension.  —  When  a  rubber  band  is  stretched,  it  is  said  to  be 
in  a  state  of  tension,  and  there  exists  between  its  molecules  a  contractile 
or  resilient  stress  which  tends  to  restore  the  body  to  its  normal  condition. 
A  rubber  balloon  inflated  with  compressed  air  is  in  a  state  of  tension  in 
every  direction. 

29.  Surface    Tension   and    Surface   Viscosity.  —  Every 
liquid  behaves  as  if  a  thin  film  forming  its  external  layer  were  ever  in  a 
state  of  tension,  or  were  exerting  a  constant  effort  to  contract.     This 
superficial  film  is  tough  or  hard  to  break  as  compared  with  the  interior 
mass.    This  property  is  called  surface  viscosity.    It  is  not  within  the  scope 
of  this  book  to  explain  how  the  molecular  forces  produce  this  result ;  it 
must  suffice  to  call  attention  to  the  peculiar  condition,  with  reference  to 
mutual  attractions,  of  those  molecules  which  compose  the  surface  film. 
In  the  interior  of  a  liquid  body  each  molecule  is  surrounded  by  other 
similar  molecules,  and  is  acted  upon  equally  in  all  directions.     At  a  free 
surface  the  molecules  can  be  acted  upon  only  by  others  lying  internal  to 
them  ;  the  outcome  of  this  is  that  it  tends  to  reduce  the  free  surface  to 
the  least  possible  area.     This  tendency  of  a  liquid  surface  to  contraction 
means  that  it  acts  like  an  elastic  membrane,  equally  stretched  in  all 
directions,  and  by  a  constant  tension. 

Experiment  18.  —  Form  a  soap-bubble  at  the  orifice  of  the  bowl 
of  a  tobacco-pipe,  and  then,  removing  the  mouth  from  the  pipe, 
observe  that  tension  of  the  two  surfaces  (exterior  and  interior)  of  the 
bubble  drives  out  the  air  from  the  interior  and  finally  the  bubble 

1  This  distinction  is  merely  a  matter  of  convenience.  It  must  not  be  supposed 
that  the  forces  of  cohesion  and  adhesion  themselves  differ. 


MOLECULAK   FORCES. 


27 


Fig.  15a. 


contracts  to  a  flat  sheet.  The  viscosity  of  a  free  surface  of  a  solution 
of  soap  in  water  is  greater  than  that  of  pure  water ;  hence  its  greater 
adaptability  to  the  formation  of  bubbles. 

As  a  consequence  of  surface  tension,  every  body  of  liquid  tends  to 
assume  a  spherical  form,  since  the  sphere  has  less  surface  than  any 
other  form  having  equal  volume.  In  large  bodies  of  liquids  the 
superior  force  of  gravitation  generally  disguises  this  effect ;  but  in 
small  bodies,  as  in  drops  of  water  or  mercury,  it  is  quite  apparent. 

3O.  Capillary  Phenomena.  —  As  a 

result  of  molecular  action  it  is  found  that  the 

surface  of  a  given  liquid  will  always  meet  a 

given  solid  at  a  definite  angle  ;  thus  the  surface 

separating  water  and  air  always  meets  clean 

glass  at  a  very  small  angle  (Fig.    15a) ;   that 

separating  mercury  and  air  meets  glass  at  an 

angle  of  about  135°.     If  clean  silver  is  substi- 
tuted for  glass,  the  first  angle  becomes  large, 

not  far  from  90°,  while  the  second  would  be 

reduced  to  zero;  in  other  words,  the  mercury 

creeps  along  the  surface  of  silver,  its  own  air-exposed  surface  being 

parallel  with  that  of  the  silver. 

From  this  it  follows,  that  it  a  glass  tube  be  dipped  into  water,  the  free 

surface  of  the  water  within  the  bore  will  be  concave,  and  the  surface 

tension  will  cause  an  upward  pull  upon  the  liquid,  and  the  liquid  will 

rise  in  the  bore  above  its  level  outside  ;  while,  if  the  tube  be  dipped  into 
mercury,  the  free  surface  of  the  mercury 
within  the  bore  will  be  convex,  and  the 
surface  tension  will  cause  a  pressure  upon 
the  liquid,  and  the  mercury  will  be  de- 
pressed below  the  level  outside.  These 
phenomena  are  known  respectively  as  capil- 
lary ascension  and  capillary  depression. 

If  the  bore  of  the  tube  is  reduced  one- 
half  in  diameter,  the  lifting  force  is  reduced 
one-half,  but  the  cross-section  will  be  re- 
duced to  one-fourth  ;  hence  in  order  that 
the  weight  of  the  liquid  lifted  may  be  one- 
half,  it  must  rise  twice  as  high  as  before. 

Thus  we  have  the  law  that  the  ascension  (or  depression)  of  a  liquid  in  a 

capillary  tube  is  inversely  proportional  to  the  diameter  of  the  bore. 


fig.  16. 


Fig.  17. 


28  MATTER,    ENERGY,    MOTION,    AND   FORCE. 

Experiment  19.  —  Take  a  clean  glass  tube  of  capillary  (i.e.  small, 
hair-like)  bore,  and  thrust  one  end  to  a  depth  of  about  a  quarter  of 
an  inch  in  water.  Does  the  water  ascend  or  descend  a  little  way  in 
the  tube  ?  What  is  the  shape  of  the  surface  of  the  water  in  the  bore 
of  the  tube  ?  Is  the  edge  of  the  water  next  the  tube  on  the  outside 
turned  up  or  down  ?  Repeat  the  experiment  with  tubes  having  bores 
of  different  size.  Do  you  notice  any  difference  in  the  phenomena  in 
the  different  tubes?  If  so,  in  which  are  the  phenomena  most 
striking  ? 

Repeat  all  the  above  experiments,  and  answer  all  the  above 
questions,  using  mercury  instead  of  water. 

Experiment  20.  —  Pour  a  little  water  into  a  U-shaped  tube  (Fig. 
16),  one  of  whose  arms  has  a  capillary  bore  ;  how  does  the  water 
behave  in  the  capillary  tube  ?     Pour  a  little  mercury  into  another 
similar  tube  (Fig.  17);  how  does  the  mercury 
behave  ?     Describe  the  upper  surfaces  of  both 
^  4        liquids. 

V  /  Experiment  21.  —  Wipe  the  surface  of   a 

\  JL  / small  cambric  needle  with  an  oily  cloth  and 

"^(BB^^^^rKf^^^BHIMi^ 

place  it  carefully  on  the  surface  of  a  cup  of 

water.     The  water  surface  will  meet  the  oily 

Tp|<r      1  "73,  ^ 

surface  at  an  angle  of  about  135°,   and   the 

surface  tension  of  the  liquid  will  act  as  a  supporting  force  as  repre- 
sented by  the  arrows  in  Figure  17a,  and  the  needle  will  float  in  a 
trough-shaped  depression  in  the  liquid  surface. 

QUESTIONS, 

1.  Why  are  pens  made  of  steel  ?     What  moves  the  machinery  of 
a  watch  ?     What  is  the  cause  of  the  softness  of  a  hair  mattress  or 
feather-bed?     On  what  does  the  entire  virtue  of  a  spring  balance 
depend  ? 

2.  What  name  would  you  give  to  the  attraction  which  causes  your 
hands  to  be  wet  by  a  liquid  ?    Is  it  a  molar  or  a  molecular  force  ? 

3.  The  tension  of  a  violin  string  is  2  pounds  ;  what  is  meant  by 
this  statement  ? 

4.  Why  are  bubbles  and  liquid  drops  round  ? 


CHAPTER  II. 

DYNAMICS*  OF  FLUIDS. 

Section  I. 

PRESSURE  IN  FLUIDS. 

31.  Cause  of  Pressure.  —  We  live  above  a  watery 
ocean  and  at  the  bottom  of  an  exceedingly  rare  and  elas- 
tic aerial  ocean,  called  the  atmosphere,  extending  with  a 
diminishing  density  to  an  undetermined  distance  into 
space.  Every  molecule,  in  both  the  gaseous  and  liquid 
oceans,  is  drawn  toward  the  earth's  center  by  gravity. 
This  gives  to  both  fluids  a  downward  pressure  upon 
everything  on  which  they  rest. 

The  gravitating  action  of  liquids  is  everywhere  appar- 
ent, as  in  the  fall  of  drops  of  rain, 
the  descent  of  mountain  streams, 
and  the  weight  of  water  in  a 
bucket.  But  to  perceive  that  air 
exerts  a  downward  pressure  re- 
quires special  manipulation.  If 
we  lower  a  pail  into  a  well,  it 
fills  with  water,  but  we  do  not 
perceive  that  it  becomes  heavier 
thereby ;  the  weight  of  the  water 
in  the  pail  is  not  felt.  But  when 
we  raise  a  pailful  out  of  the  water,  it  suddenly  appears 

1  Dynamics  is  the  science  which  investigates  the  action  of  force. 


30 


DYNAMICS    OF   FLUIDS. 


heavy.  If  we  could  raise  a  pailful  of  air  out  of  the  ocean  of 
air,  might  not  the  weight  of  the  air  become  perceptible  ? 
If  we  dive  to  the  bottom  of  a  pond  of  water,  we  do  not 
feel  the  weight  of  the  pond  resting  upon  us.  We  do  not 
feel  the  weight  of  the  atmospheric  ocean  resting  upon  us ; 
but  we  should  remember  that  our  situation  with  reference 
to  the  air  is  like  that  of  a  diver  with  reference  to  water. 

32.    Gravity  causes  Pressure  in  All  Directions. 

Experiment  22.  —  Fill  two  glass  jars  (Fig.  18)  with  water,  A  hav- 
ing a  glass  bottom,  B  a  bottom  provided 
by  tying  a  piece  of  sheet-rubber  tightly 
over  the  rim.  Invert  both  in  a  larger 
vessel  of  water,  C.  The  water  in  A  does 
riot  feel  the  downward  pressure  of  the 
air  directly  above  it,  the  pressure  being 
sustained  by  the  rigid  glass  bottom.  But 
it  indirectly  feels  the  pressure  of  the  air 
on  the  surface  of  the  water  in  the  open 
vessel,  and  it  is  this  pressure  that  sus- 
tains the  water  in  the  jar.  But  the 
rubber  bottom  of  the  jar  B  yields  some- 
what to  the  downward  pressure  of  the 
air,  and  is  forced  inward. 
Experiment  23.  —  Fill  a  glass  tube,  D,  with  water,  keeping  one 

end  in  the  vessel  of  water,  and  a  finger 

tightly  closing  the  upper  end.     Why 

does  not  the  water  in  the  tube  fall? 

Remove  your  finger  from  the   closed 

end.     Why  does  the  water  fall  ? 

Experiment  24.  —  Fill    (or  partly 

•fill)  a  tumbler  with  water,  cover  the 

top  closely  with   a  card   or  writing-paper,  hold  the  paper  in  place 

with  the  palm  of  the  hand,  and  quickly  invert  the  tumbler  (Fig.  19). 

Why  does  not  the  water  fall  out? 
Experiment  25.  —  Force  the  piston  A  (Fig.  20)  of  the  seven-in-one 

apparatus  (so  called  from  the  number  of  experiments  that  may  be 

performed  with  one  piece  of  apparatus)  quite  to  the  closed  end  of  the 


Fig.  19. 


Fig.  30. 


PRESSURE   IN   FLUIDS. 


31 


hollow  cylinder,  and  close  the  stop-cock  B.  Try  to  pull  the  piston  out 
again.  Why  do  you  not  succeed?  Hold  the  apparatus  in  various 
positions,  so  that  the  atmosphere  may  press  down, 
laterally,  and  up  against  the  piston.  Do  you  dis- 
cover any  difference  in  the  pressure  which  it  re- 
ceives from  different  directions  ? 

Experiment  26.  — Force  a  tin  pail  (Fig.  21), 
having  a  hole  in  its  bottom,  as  far  as  possible  into 
water,  without  allowing  water  to  enter  at  the  top. 
A  stream  of  water  spurts  through  the  hole.  Why  ? 
Why  does  it  require  so  much  effort  to  force  the  pail 
Fig.  21.  down  into  the  water  ? 

33.  Comparison  of  Pressure  at  the  Same  Depth  in 
Different  Directions. 

Experiment  27. —  Take  a  glass  tube  about  30  inches  long  and 
one-fourth  inch  bore,  and  bend  it  into  the  shape  of  A  (Fig.  22).  Also 
prepare  tubes  like  B  and  C.  Let  the 
bend  a  be  about  half  full  of  water. 
Slowly  lower  the  end  n  into  a  tumbler 
filled  with  water.  The  water  presses 
up  against  the  air  in  the  tube,  and 
the  air  transmits  the  pressure  to  the 
liquid  in  the  bend.  How  is  the  pres- 
sure affected  by  depth?  Does  it 
increase  as  the  depth  ? 

Experiment  28.  —  Connect  c  with 
d  by  means  of  a  rubber  tube,  and 
lower  the  extremity  m  into  the  tum- 
bler of  water.  As  the  tube  is  turned 
up,  the  water  must  now  press  down 
the  tube  against  the  air.  Does  the  downward  pressure  increase  as 
the  depth? 

Experiment  29.  —  Connect  e  with  c,  and  lower  o  into  the  water. 
The  water  now  presses  laterally  (sidewise)  against  the  air.  Does  the 
lateral  pressure  increase  as  the  depth? 

Experiment  30.  —  Fill  two  tumblers  with  water,  and  lower  n  into  one 
and  o  into  the  other,  keeping  both  extremities  at  the  same  depth 
in  the  liquids.  How  is  the  liquid  in  the  bend  a  affected?  How  do 


Fig.  22. 


32 


DYNAMICS   OF  FLUIDS. 


tig.  £3. 


the  upward  and  lateral  pressures  at 
the  same  depth  compare  ? 

Experiment  31.  —  Once  more  con- 
nect c  with  d,  and  lower  n  and  m  to 
the  same  depth  into  the  water  in  the 
two  tumblers.  How  do  the  upward 
and  downward  pressures  at  the  same 
depth  compare  ?  At  the  same  depth  is 
pressure  equal  in  all  directions  ? 

Experiment  32.  —  Connect  the  two 
brass  tubes  at  the  extremities  F  and  G 
(Fig.  23).  Fill  the  cup  of  the  (eight- 
in-one)  apparatus  with  water,  and  re- 
move the  caps  A,  B,  C,  and  D  from 
the  branch  tubes,  so  as  to  permit  water 
to  escape  from  the  orifices  at  their 
ends.  Does  the  water  issuing  from 
these  orifices  show  a  lateral  pressure  ? 
What  difference  do  you  observe  in  the 
flow  of  water  from  the  different 
orifices?  How  do  you  account  for 
it? 

The  results  of  experiments 
thus  far  show  that  at  every 
point  in  a  body  of  fluid  gravity 
causes  pressure  to  be  exerted 
equally  in  all  directions,  and 
that  in  liquids  the  pressure  in' 
creases  as  the  depth  increases. 


MEASUREMENT  OF  ATMOSPHEEIC  PRESSURE. 


33 


Section  II. 


Fig.  24. 


MEASUREMENT  OF  ATMOSPHERIC  PRESSURE,  BAROMETERS. 

34.    How  Atmospheric  Pressure  is  Measured. 

Experiment    33    (preliminary).  —  Take    a    U-shaped   glass  tube 

(Fig.    24),    half  fill    it  with 

water,  close  one  end  with  a 

thumb,  and  tilt  the  tube  go 

that  the  water  will  run  into 

the  closed    arm    and    fill  it; 

then  restore  it  to  its  original 

vertical  position.     Why  does 

not  the  water  settle    to  the 

same  level  in  both  arms  ? 

Figure  25  represents  a  U-shaped  glass  tube  closed  at  one  end,  34 
inches  in  hight,  and  with  a  bore  of  1  square  inch 
section.  The  closed  arm  having  been  filled  with 
mercury,  the  tube  is  placed  with  its  open  end  up- 
ward, as  in  the  cut.  The  mercury  in  the  closed  arm 
sinks  about  2  inches  to  A,  and  rises  2  inches  in  the 
open  arm  to  C ;  but  the  surface  A  is  30  inches 
higher  than  the  surface  C.  This  can  be  accounted 
for  only  by  the  atmospheric  pressure.  The  column 
of  mercury  BA,  containing  -30  cubic  inches,  is  an 
exact  counterpoise  for  a  column  of  air  of  the  same 
diameter  extending  from  C  to  the  upper  limit  of 
the  atmospheric  ocean,  —  an  unknown  hight. 

The  weight  of  the  30  cubic  inches  of  mercury 
in  the  column  BA  is  about  15  pounds.  Hence 
the  weight  of  a  column  of  air  of  1  square-inch  sec- 
tion, extending  from  the  surface  of  the  sea  to  the 
upper  limit  of  the  atmosphere,  is  about  15  pounds. 
But  in  fluids  gravity  causes  equal  pressure  in  all 
directions.  Hence,  at  the  level  of  the  sea,  all  bodies 

are  pressed  upon  in  all  directions  by  the  atmosphere,  with  a  force  of  about 

15  pounds  per  square  inch,  or  about  one  ton  per  square  foot. 


Fig.  35. 


34 


DYNAMICS   OF   FLUIDS. 


A  pressure  of  15  pounds  per  square  inch  is  quite  generally  adopted 
as  a  unit  of  gaseous  pressure,  and  is  called  an  atmosphere. 


Fig.  »6. 

35.  Barometer.  —  The  hight  of  the 
column  of  mercury  supported  by  atmos- 
pheric pressure  is  quite  independent,  how- 
ever, of  the  area  of  the  surface  of  the  mer- 
cury pressed  upon ;  hence  the  apparatus 
is  more  conveniently  constructed  in  the 
form  represented  in  Figure  26. 

A  straight  tube  about  34  inches  long 
is  closed  at  one  end  and  filled  with  mer- 
cury. A  finger  tightly  closing  the  open 
end,  the  tube  is  inverted,  and  this  end  is 
inserted  in  a  vessel  of  mercury  and  the 
finger  is  withdrawn,  when  the  mercury 
sinks  until  there  is  equilibrium  between 
the  downward  pressure  of  the  mercurial  column  AB  and 


BAROMETERS.  35 

the  pressure  of  the  atmosphere.  An  apparatus  designed 
to  measure  atmospheric  pressure  is  called  a  barometer 
(pressure-measurer).  A  common  form  of  barometer  is 
represented  in  Figure  27.  Beside  the  tube  and  near  its 
top  is  a  scale  graduated  in  inches  or  centimeters,  indi- 
cating the  hight  of  the  mercurial  column.  For  ordinary 
purposes  this  scale  needs  to  have  only  a  range  of  three  or 
four  inches,  so  as  to  include  the  maximum  fluctuations 
of  the  column. 

The  hight  of  the  barometric  column  is  subject  to  fluc- 
tuations ;  this  shows  that  the  atmospheric  pressure  is  sub- 
ject to  variations.  The  barometer  is  always  a  faithful 
monitor  of  all  changes  in  atmospheric  pressure.  It  is  also 
serviceable  as  a  weather  indicator.  It  does  not  indicate 
weather  that  is  present,  but  foretells  coining  weather. 
Not  that  any  particular  point  at  which  mercury  may  stand 
foretells  any  particular  kind  of  weather,  but  any  sudden 
change  in  the  barometer  indicates  a  change  in  the  weather. 
A  rapid  fall  of  mercury  generally  forebodes  a  storm, 
while  a  rising  column  indicates  clearing  weather. 

36.  Aneroid  Barometer.  —  The  aneroid  (without  moisture) 
barometer  employs  no  liquid.  It  contains  a  cylindrical  box,  D  (Fig. 
28),  having  a  very  flexible  top.  The  air  is  partially  exhausted  from 
within  the  box.  The  varying  atmospheric  pressure  causes  this  top  to 
rise  and  sink  much  like  the  chest  of  man  in  breathing.  Slight  move- 
ments of  this  kind  are  communicated  by  means  of  multiplying-apparatus 
(apparatus  by  means  of  which  a  small  movement  of  one  part  is  mag- 
nified into  a  large  movement  of  another  part)  to  the  index  needle  A. 
The  dial  is  graduated  to  correspond  with  a  mercurial  barometer.  The 
observer  turns  the  button  C  and  brings  the  brass  needle  B  over  the  black 
needle  A,  and  at  his  next  observation  any  departure  of  the  latter  from 
the  former  will  show  precisely  the  change  which  has  occurred  between 
the  observations. 

The  aneroid  can  be  made  more  sensitive  (i.e.  so  as  to  show  smaller 
changes  of  atmospheric  pressure)  than  the  mercurial  barometer.  If  a 


36  DYNAMICS    OF    FLUIDS. 

barometer  is  carried  up  a  mountain,  it  is  found  that  the  mercury  con- 
stantly falls  as  the  ascent  increases.  Roughly  speaking,  the  barometer 
falls  one  inch  for  every  900  feet  of  ascent.  Really,  in  consequence  of  the 
rapid  increase  of  the  rarity  of  the  air,  the  rate  of  fall  diminishes  as  you 
ascend.  It  is  obvious  that  the  barometer  will  serve  to  measure  approxi- 
mately the  hights  of  mountains  by  ascertaining  the  barometric  readings 
on  the  summit  and  at  sea-level. 

If  a  mercurial  barometer  stand  at  760 mm  on  the  floor,  the  same  barom- 
eter on  the  top  of  a  table  lm  high  should  stand  at  a  hight  of  759.91mm, 

a  change  scarcely  perceptible.  The  an- 
eroid is,  however,  sometimes  made  so 
sensitive  that  the  change  of  pressure  ex- 
perienced in  this  short  distance  is  ren- 
dered quite  perceptible. 

The  barometer  is  sometimes  called  a 
"  weather-glass,"  chiefly  because  its  scale 
frequently  bears  the  words  /air,  rainy, 
storm,  etc.  These  words  are  very  objec- 
tionable, since  they  are  totally  wrong 
from  a  meteorological  point  of  view.  To 
form  a  forecast  of  the  weather  of  much 
Fi  88  value,  a  barometer,  a  thermometer,  and 

a  hygrometer  must  be  consulted,  and  one 

must  be  familiar  with  the  laws  which  govern  the  relations  between 
atmospheric  pressure,  temperature,  moisture,  etc. 

Many  physical  operations  require  a  standard  pressure  for  reference. 
The  standard  generally  adopted  is  the  pressure  exerted  by  a  column  of 
pure  mercury  at  0°  C.  and  76 cm  (29.922  inches)  high,  which  is  about  the 
average  hight  of  the  barometric  column  at  sea-level  in  latitude  45°.  The 
pressure  corresponding  to  this  hight  is  1033.3  grams  per  square  centi- 
meter, or  14.69  pounds  per  square  inch. 

The  shading  in  Figure  29  is  intended  to  indicate  roughly  the  variation 
in  the  density  of  the  air  at  different  elevations  above  sea-level.  The 
figures  in  the  left  margin  show  the  hight  in  miles;  those  in  the  first 
column  on  the  right,  the  corresponding  average  hight  of  the  mercurial 
column  in  inches  ;  and  those  in  the  extreme  right,  the  density  of  the  air 
compared  with  its  density  at  sea-level. 

If  an  opening  could  be  made  in  the  earth  35  miles  in  depth  below  the 
sea-level,  it  is  caleulated  that  the  density  of  the  air  at  the  bottom  would 
be  1,000  times  that  at  sea-level,  so  that  water  would  float  in  it.  Air  has 
been  compressed  to  this  density. 


BAROMETERS. 


37 


To  what  hight  the  atmosphere  extends  is  unknown.     It  is  variously 
estimated  at  from  50  to  200  miles.     If  the  aerial  ocean  were  of  uniform 


-nfoa 


Fig.  29. 

density,  and  of  the  same  density  that  it  is  at  sea-level,  its  depth  would  be 
a  little  short  of  five  miles.  Certain  peaks  of  the  Himalayas  would  rise 
above  it. 

QUESTIONS. 

1.  What  is  the  pressure  per  square  centimeter  when  the  barometric 
reading  is  770  mm? 

2.  At  a  certain  point  on  a  mountain  the  average  barometric  hight 
is  24.5  inches  ;    what   is  the  average  atmospheric  pressure  at  this 
point  ? 

3.  What  is  the  approximate  elevation  of  the  point  mentioned  in 
the  last  question  above  the  sea-level? 

4.  Consult  Figure  29,  and  determine  what  portion  of  the  matter  of 
the  atmospheric  ocean  must  be  below  the  summit  of  Mt.  Blanc. 


38  DYNAMICS    OF   FLUIDS. 


Section  III. 

COMPRESSIBILITY   AND    ELASTICITY    OF    GASES.  —  BOYLE'S 

LAW. 

37.  Compressibility  of  Gases.  —  The  increase  of  pres- 
sure attending  the  increase  in  depth,  in  both  liquids  and 
gases,  is  readily  explained  by  the  fact  that  the  lower  layers 
of  fluids  sustain  the  weight  of  all  the  layers  above.     Con- 
sequently, if  the  body  of  fluid  is  of  uniform  density,  as  is 
very  nearly  the  case  in  liquids,  the  pressure  will  increase 
in  nearly  the  same  ratio  as  the  depth  increases.     But  the 
aerial  ocean  is  far  from  being  of  uniform  density,  in  con- 
sequence of  the  extreme  compressibility  of  gaseous  matter. 
The  contrast  between  water  and  air,  in  this  respect,  may 
be  seen  in  the  fact  that  water  subjected  to  a  pressure  of 
one  atmosphere  is  compressed  0.0000457  its  volume  ;  under 
the  same  circumstances,  air  is  compressed  one-half.     For 
most  practical  purposes,   we  may  regard  the    density  of 
water  at  all  depths  as  uniform,  while  it  is  far  otherwise  in 
large  masses  of  gases. 

38.  Elasticity    of    Gases.  —  Closely     allied    to    com- 
pressibility is  the   elasticity  of  gases,  or  their  power  to 
recover  their  former  volume  after  compression.     The  elas- 
ticity of  all  fluids  is  perfect.     By  this  is  meant,  that  the 
force  exerted  in  expansion  is  equal  to  the  force  used  in 
compression ;    and   that,  however   much   a  fluid   is   com- 
pressed, it  will  always  completely  regain  its  former  bulk 
when  the  pressure   is   removed.      Hence   the   barometer 
which  measures  the  compressing  force  of  the  atmosphere 
also  measures  at  the  same  time  the  elastic  force  (i.e.  the 


COMPRESSIBILITY   AND   ELASTICITY   OF   GASES. 


39 


tension  or  expansive  force)  of  the  air.  Liquids  are  per- 
fectly elastic ;  but,  inasmuch  as  they  are  perceptibly  com- 
pressed only  under  tremendous  pressure,  they  are  regarded 
as  practically  incompressible,  and  so  it  is  rarely  necessary 
to  consider  their  elasticity.  It  has  already  been  stated 
that  matter  in  a  gaseous  state  expands  indefinitely  unless 
restrained  by  external  force.  The  atmosphere  is  con- 
fined to  the  earth  by  the  force  of  gravity. 


Experiment  34.  —  Force  the  piston  of  the  seven-in-one  apparatus 

two-thirds  the  way  into  the  cylinder,  and  close  the  aperture.    Support 

the  apparatus  on  blocks,  with  the  piston  upwards,  remove  the  handle, 

and  place  a  weight  on  the  piston,  and  place  the 

whole  under  the  receiver  of  an  air-pump.     Exhaust 

the  air  from  the  receiver ;  the  outside  pressure  of 

the  air  being  partially  removed,  the  unbalanced 

force  (i.e.  the  tension)  of  the  air  enclosed  within 

the  cylinder  will  cause  the  piston  to  rise,  and  raise 

the  weight. 

Experiment  35.  —  Arrange  the  same  apparatus 

as  in  Figure  30.     Attach  a  small  rubber  tube  to 

the  short  tube,  and  suck  as  much  air  out  of  the 

cylinder  as  possible.  The  air  within,  being  rarefied, 

exerts  less  pressure,  and  the  unbalanced  outside 
pressure  forces  the  piston  into 
the  cylinder,  raising  the  weight. 
A  very  much  heavier  weight  may  be  raised  if  the 
rubber  tube  connects  the  apparatus  with  an  air- 
pump. 

Experiment  36.  —  Take  a  glass  tube  (Fig.  31) 
having  a  bulb  blown  at  one  end.  Nearly  fill  it 
with  water,  so  that  when  inverted  there  will  be  only 
a  bubble  of  air  in  the  bulb.  Insert  the  open  end 
in  a  glass  of  water,  place  under  a  receiver,  and 
exhaust.  Nearly  all  the  water  will  leave  the  bulb 

and  tube.     Why?    What  will  happen  when  air  is  admitted  to  the 

receiver  ? 


Fig.  30. 


Fig.  31. 


40 


DYNAMICS    OF    FLUIDS. 


-Bi 


39.  Boyle's  (or  Mariotte's)  Law. 

Experiment  37.  —  Take  a  bent  glass  tube  (Fig.  32),  the  short  arm 
being  closed,  and  the  long  arm,  which  should  be  at  least  34  inches 
(85cm)  long,  being  open  at  the  top.    Pour  mercury 
into  the  tube  till  the  surfaces  in  the  two  arms  are  at 
the  same  level  AB.    The  body  of  air  to  be  experi- 
mented with  is  in  the  short  arm  between  A  and  C. 
The  dimensions  of  this  body  can  vary  only  in 
hight ;  hence  its  hight,  H,  may  represent  its  volume. 
Measure  H  (i.e.  the  distance  between  A  and  C)  and 
regard  the  number  of  inches  (or  centimeters)  as 
representing  the  volume,  V.     Its  pressure,  P,  evi- 
dently is  the  same  as  that  of  the  atmosphere  at  the 
time.  Consult  a  barometer,  and  ascertain  the  hight 
of  the  barometric  column  ;  represent  this  hight  by 
P.     Pour  a  little  mercury  into  the  tube  ;  the  mer- 
cury rises  (say)  to  Al  and  Bj .     Measure  the  verti- 
cal distance  between  A1  and  C  ;  this  number  repre- 
sents the  volume,  Vx,  of  the  body  of   air  now. 
Measure  the  vertical  distance  between  A1  and  Bx ; 
this  number  represents  the  increase  in  pressure, 
which,  added  to  P,  gives  its  present  pressure,  P1 . 
Now  pour  more  mercury  into  the  tube,  so  that  it  will  rise  to  (say) 
A2  and  B2 .     Determine  as  before  the  new  volume,  V2 ,  and  the  new 
pressure,  P2 .     So  continue  to  add  mercury  a  third  and  a  fourth  time, 
and  get  new  values  for  the  volume,  V3  and  V4,  and  for  the  pressure, 
P3  and  P4 .     Arrange  the  results  as  follows  :  — 

V  = P  = v  X  P  = 

Va  ='.'.'.'.'.  P!  = V2  X   P2  = 

etc.  etc. 

It  will  be  found  that  the  series  of  products  in  the  last  column  are 
approximately  equal  (due  allowance  being  made  for  errors  in  meas- 
urement, etc.) ;  consequently  the  product  of  the  volume  of  a  body  of 
gas  multiplied  by  its  pressure  is  constant,  and  the  volume  varies 
inversely  as  its  pressure.  Hence  the  (Boyle's)  law  :  — 

The  volume  of  a  body  of  gas  at  a  constant  temperature  varies  inversely 
as  its  pressure,  density,  and  elasticity. 


B 


Fig.  32. 


RAREFYING   AND    CONDENSING   INSTRUMENTS.         41 

For  many  years  after  the  announcement  of  this  law  it  was  believed  to  be  rigor- 
ously correct  for  all  gases  ;  but  more  recently  more  precise  experiments  have  shown 
that  it  is  approximately  but  not  rigidly  true  for  any  gas.  There  is  a  limit  beyond 
which  this  law  does  not  hold.  This  limit  is  soonest  reached  with  those  gases,  like 
carbon-dioxide,  chlorine,  etc.,  that  are  most  readily  liquefied.  A  gas  conforms  more 
nearly  to  Boyle's  law,  in  proportion  as  it  is  farther,  as  regards  both  pressure  and 
temperature,  from  its  liquefying  point.  As  a  gas  approaches  this  point  its  density 
increases  more  rapidly  than  its  elasticity. 


Section  IV. 

INSTRUMENTS    USED    FOR    RAREFYING    AND    CONDENSING 

AIR. 

4O.  The  Air-Pump.  —  The  air-pump,  as  its  name  im- 
plies, is  used  to  withdraw  air  from  a  closed  vessel.  Figure 
33  will  serve  to 
illustrate  its  op- 
eration. R  is  a 
glass  receiver  from 
which  air  is  to  be 
exhausted.  B  is  a 
hollow  cylinder  of 
brass,  called  the 
pump-barrel.  The 
plug  P,  called  a 
piston,  is  fitted  to 
the  interior  of  the 
barrel,  and  can  be  ms-  33- 

moved  up  and  down  by  the  handle  H ;  s  and  t  are  valves. 
A  valve  acts  on  the  principle  of  a  door  intended  to 
open  or  close  a  passage.  If  you  walk  against  a  door 
on  one  side,  it  opens  and  allows  you  to  pass ;  but 
if  you  walk  against  it  on  the  other  side,  it  closes  the 
passage,  and  stops  your  progress.  Suppose  the  piston 
to  be  in  the  act  of  descending ;  the  compression  of 


42  DYNAMICS    OF   FLUIDS. 

the  air  in  B  closes  the  valve  £,  and  opens  the  valve  s,  and 
the  enclosed  air  escapes.  After  the  piston  reaches  the 
bottom  of  the  barrel,  it  begins  its  ascent.  This  would 
cause  a  vacuum  between  the  bottom  of  the  barrel  and  the 
ascending  piston  (since  the  unbalanced  pressure  of  the 
outside  air  immediately  closes  the  valve  *),  but  the  pressure 
of  the  air  in  the  receiver  R  opens  the  valve  t  and  fills  this 
space.  As  the  air  in  R  expands,  it  becomes  rarefied  and 
exerts  less  pressure.  The  external  pressure  of  the  air  on 
R,  being  no  longer  balanced  by  the  pressure  of  the  air 
within,  presses  the  receiver  firmly  upon  the  plate  L.  Each 
repetition  of  a  double  stroke  of  the  piston  removes  a  por- 
tion of  the  air  remaining  in  R.  The  air  is  removed  from 
R  by  its  own  expansion.  However  far  the  process  cf 
exhaustion  may  be  carried,  the  receiver  will  always  be 
filled  with  air,  although  it  may  be  exceedingly  rarefied. 
The  operation  of  exhaustion  is  practically  ended  when  the 
pressure  of  the  air  in  R  becomes  too  feeble  to  lift  the  valve  t. 
Sometimes  another  receiver,  D,  is  used,  opening  into  the 
tube  T,  that  connects  the  receiver  with  the  barrel.  Inside 
the  receiver  is  placed  a  barometer.  It  is  apparent  that  air 
is  exhausted  from  D  as  well  as  from  R  ;  and,  as  the  pres- 
sure is  removed  from  the  surface  of  the  mercury  in  the 
cup,  the  barometric  column  falls  ;  so  that  the  barometer 
serves  as  a  gauge  to  indicate  the  approximation  to  a 
vacuum.  For  instance,  when  the  mercury  has  fallen 
380mm  (15  inches),  one-half  of  the  air  has  been  removed. 

41.  The  Mercury  Air-Pump.  —  In  recent  years  the 
so-called  mercury  air-pump  has  largely  displaced  the  pump 
described  above,  since  it  is  capable  of  producing  a  much 
greater  rarefaction.  In  brief,  it  makes  use  of  the  Torri- 
cellian vacuum,  such  as  is  formed  in  the  top  of  a  barometer 
tube.  On  account  of  its  simplicity,  the  Geissler  pump, 


RAREFYING   AND   CONDENSING   INSTRUMENTS.        43 


Fig.  34 


the  first  of  the  kind  invented,  is  chosen  for  illustration. 
A  (Fig.  34)  is  a  glass  tube  more  than  thirty-four  inches 
long,  having  a  globe-like  enlargement  B  of  about  a  liter 
capacity.  Above  this  globe 
leads  a  tube  containing  a 
three-way  stop-cock  and  a 
branch  tube  D.  By  means 
of  this  stop-cock  B  may  be 
placed  in  communication 
either  through  D  with  the 
atmosphere,  as  shown  in  M 
(Fig.  35),  or  through  E 
with  the  receiver  to  be  ex- 
hausted, as  shown  in  N. 
Connected  with  the  lower 
end  of  A  by  means  of  a  thick  rubber  tube  is  a  vessel  G 
containing  mercury.  The  pump  is  operated  as  follows  : 
C  is  turned  as  in  M,  G  is  raised  so  that  the  mercury  will 
flow  from  it  into  B  and  fill  it,  the  air  escaping  through  D. 
Then  the  stop-cock  is  placed  as  in  N,  and  G  is  lowered  so 
as  to  allow  the  mercury  to  flow  back  into  it.  A  Torricel- 
lian vacuum  would  be  formed  in  B  were  it  not  in  commu- 
nication through  E  with  the  receiver.  AS  it  is,  the  air  in 
this  space  expands  and  fills  B,  and  is  thus  to  this  extent 
rarefied.  By  a  sufficient  number  of  repetitions  of  this 
process,  a  very  high  vacuum  is  obtainable.  There  are  many 
modifications  of  this  pump,  in  some  of  which  the  stop-cock 
is  dispensed  with,  and  consequently  the  trouble  of  operat- 
ing it  is  avoided.  With  the  common  pump  a  vacuum  of 
a  millimeter  of  mercury  is  considered  exceedingly  good  ; 
but  with  a  mercury  pump  it  is  easy  to  obtain  a  vacuum  of 
.00076  of  a  millimeter,  which  represents  about  one  mil- 
lionth the  normal  pressure  of  the  atmosphere. 


44 


DYNAMICS    OF  FLUIDS. 


42.    Condenser. 

Experiment  39.  —  Blow  into  a  U-shaped  glass  tube  open  at  both 
ends  and  partly  filled  with  mercury.  Measure  the  vertical  distance 
between  the  two  surfaces  of  mercury  and  calcu- 
late the  excess  of  the  pressure  of  the  condensed 
air  above  that  of 
the  atmospheric 
pressure. 

Figure  6,  page 
5,  represents  in 
perspective,  and 
Figure  36,  in  sec- 
tion, an  appara- 
tus for  condens- 
ing air,  called  a 
condenser.  Its 
Fig.  36.  construction  is 

like  that  of  the  barrel  of  an  air-pump,  except  that  the 
direction  in  which  the  valves  open  is  reversed. 

Experiment  40.  —  Place  a  block  having  a  wide  platform  at  one 
end  on  the  piston  of  the  seven-in-one  apparatus.  On  the  platform  let 
a  child  stand.  By  means  of  a  condensing  syringe  (Fig.  6),  connected 
by  a  rubber  tube  with  the  seven-in-one  apparatus  (Fig.  37),  condense 
the  air  in  the  cylinder  and  raise  the  child. 


Section  V. 

APPARATUS   FOR   RAISING   LIQUIDS. 

43.  Lifting  or  Suction  Pump.  —  The  common  lifting- 
pump  is  constructed  like  the  barrel  of  an  air-pump.  Fig- 
ure 38  represents  the  piston  B  in  the  act  of  rising.  As 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSICS 
APPARATUS  FOE  RAISING  LIQUIDS. 


45 


the  air  is  rarefied  below  it,  water  rises  in  consequence 
of  atmospheric  pressure  on  the  water  in  the  well,  and 
opens  the  lower  valve  D.  Atmospheric  pressure  closes 


Fig.  39. 


Fig.  40. 


the  upper  valve  C  in  the  piston.  When 
the  piston  is  pressed  down  (Fig.  39),  the 
lower  valve  closes,  the  upper  valve  opens, 
and  the  water  between  the  bottom  of  the 
barrel  and  the  piston  passes  through  the 
Fig.  ss.  upper  valve  above  the  piston.  When 

the  piston  is  raised  again  (Fig.  40),  the  water  above  the 

piston  is  raised  and  discharged  from  the  spout. 
The  liquid  is  sometimes  said  to  be  raised 

in  a  lifting-pump  by  the  "force  of  suction." 

Is  there  such  a  force? 


Experiment  41.  —  Bend  a  glass  tube  into  a  U-shape, 
with  unequal  arms,  as  in  Figure  41.     Fill  the  tube  with 
the  liquid  to  the  level  cb.    Close  the  end  b  with  a  finger, 
and  try  to  suck  the  liquid  out  of  the  tube.     You  find        Vis»  *!• 
it  impossible.    Remove  the  finger  from  b,  and  you  can  suck  the  liquid 
out  with  ease.    Why? 


46 


DYNAMICS   OF  FLUIDS. 


44.  Force-Pump.  —  The  piston  of  a  force-pump  (Fig. 
42)  has  no  valve,  but  a  branch  pipe  a  leads  from  the  lower 
part  of  the  barrel  to  an  air-condensing  chamber  £>,  at  the 
bottom  of  which  is  a  valve  c,  opening  upward.  As  the 
piston  is  raised,  water  is  forced  up  through 
the  valve  d,  while  water  in  b  is  pre- 
vented from  returning  by  the  valve  c. 
When  the  piston  is  forced  down,  the 
valve  d  closes,  the  valve  c  opens,  and  the 
water  is  forced  into  the  chamber  6,  con- 
densing the  air  above  the  water.  The 
elasticity  of  the  condensed  air  forces  the 
water  out  of  the  tube  e  in  a  continuous 
stream. 

QUESTIONS  AND  PROBLEMS. 

1.  What  force  is  the  cause  of  fluid  pressure  ? 

2.  Why  does  not  a  person  at  the  bottom  of  a 
pond  feel  the  weight  of  the  water  above  him  ? 

3.  An  aeronaut  finds  that  on   the  earth  his 
barometer  stands  at  30  inches.     He  ascends  in  a 
balloon  until  the  barometer  stands  at  20  inches. 
About  how  high  is  he  ?    What  is  the  pressure  of 
the  atmosphere  at  his  elevation  ? 

4.  When  a  barometer  stands  at  30  inches,  the 
atmospheric  pressure  is  14.7  pounds.     What  is 

the  atmospheric  pressure  when  the  barometer  stands  at  29  inches  ? 

5.  Why  is  a  barometer  tube  closed  at  the  top  ?    Why  must  air  come 
in  contact  with  the  mercury  at  the  bottom  ? 

6.  What  would  be  the  effect  on  an  aneroid  barometer  if  it  were 
placed  under  the  receiver  of  an  air-pump,  and  one  or  two  strokes 
of  the  pump  were  made? 

7.  Suppose  a  rubber  foot-ball  to  be  partially  inflated  with  air  at 
the  surface  of  the  earth;  what  would  happen  if  it  were  taken  up  in  a 
balloon  ? 

8.  Mercury  is  13.6  times  denser  than  water.     When  a  mercurial  ba- 


Fig.  43. 


TRANSMISSION  OF  EXTERNAL  PRESSURE.  47 

rometer  stands  at  30  inches,  how  high  would  a  water  barometer  stand  ? 
How  high,  theoretically,  could  mercury  be  raised  on  such  a  day  by 
suction?  How  high  coukl  water  be  raised  by  the  same  means?  How 
many  times  higher  can  water  be  raised  by  a  suction-pump  than  mer- 
cury? 

9.  What  is  that  which  is  sometimes  called  the  "force  of  suction  "? 

10.  The  area  of  one  side  of  the  piston  of  the  seven-in-one  apparatus 
is  about  26  square  inches.     Suppose  the  piston  to  be  forced  into  the 
cylinder  so  as  to  drive  out  all  the  air,  and  then  the  orifice  to  be  closed ; 
what  force  would  be  required  to  draw  the  piston  out,  when  the  barom- 
eter stands  at  30  inches  ?    What  force  would  be  required  on  the  top  of 
a  mountain  where  the  barometer  stands  r,,t  15  inches  ? 

11.  Water  is  raised  the  larger  part  of  the  distance  in  our  lifting- 
pumps  by  atmospheric  pressure ;   why,  then,  is  not  such  a  pump  a 
labor-saving  instrument? 

12.  If  water  is  to  be  raised  from  a  well  50  feet  deep,  how  high  must 
it  be  lifted,  and  how  long  must  the  barrel  be? 


Section  VI. 

TRANSMISSION  OF  EXTERNAL  PRESSURE. 

45.  Pressure  Transmitted  TJndiminished  in  All  Direc- 
tions. 

Experiment  42.  —  Fill  the  glass  globe  and  cylinder  (Fig.  43)  with 
water,  and  thrust  the  piston  into  the  cylinder.  Jets  of  water  will  be 
thrown  not  only  from  that  aperture  a  in  the  globe  toward  which  the 
piston  moves  and  the  pressure  is  exerted,  but  from  apertures  on  all 
sides.  Furthermore,  the  streams  extend  to  equal  distances  in  every 
direction. 

It  thus  appears  that  external  pressure  is  exerted  not 
alone  upon  that  portion  of  the  liquid  that  lies  in  the 
path  of  the  force,  but  it  is  transmitted  equally  to  all 
parts  and  in  all  directions. 


48 


DYNAMICS   OF   FLUIDS. 


Experiment  43.  —  Measure  the  diameter  of  the  bore  of  each  arm 
of  the  glass  U-tube  (Fig.  44).     We  will  suppose,  for  illustration,  that 

the  diameters  are  respectively  40mm  and 
10mm;  then  the  areas  of  the  transverse 
sections  of  the  bores  will  be  402 : 102  =  16 ; 
that  is,  when  the  tube  contains  a  liquid, 
the  area  of  the  free  surface  of  the  liquid 
in  the  large  arm  will  be  16  times  as  great 
as  that  in  the  small  arm.  Pour  mercury 
into  the  tube  until  it  stands  about  lcm 
above  the  bottom  of  the  large  arm.  The 
mercury  stands  at  the  same  level  in  both 
arms.  Pour  water  upon  the  mercury  in 
the  large  arm  until 
this  arm  lacks  only 
about  lcm  of  being 
full.  The  pressure  of 
the  water  causes  the 
mercury  to  rise  in  the 
small  arm,  and  to  be 
depressed  in  the  large 
arm.  Pour  water  very 
slowly  into,  the  small 
arm  from  a  beaker  having  a  narrow  lip,  until  the  surfaces  of  the  water 
in  the  two  arms  are  on  the  same  level.  It  is  evident  that  the  quantity 
of  water  in  the  large  arm  is  16  times  as  great  as  that  in  the  small  arm. 
This  phenomenon  appears  paradoxical  (apparently  contrary  to  the  natu- 
ral course  of  things),  until  we  master  the  important  hydrostatic  princi- 
ple involved.  We  must  not  regard  the  body  of  mercury  as  serving  as 
a  balance  beam  between  the  two  bodies  of  water,  for  this  would  lead 
to  the  absurd  conclusion  that  a  given  mass  of  matter  may  balance  an- 
other mass  16  times  as  great.  We  may  best  understand  this  phenom- 
enon by  imagining  the  body  of  liquid  in  the  large  arm  to  be  divided 
into  cylindrical  columns  of  liquid  of  the  same  size  as  that  in  the  small 
arrn.  There  will  evidently  be  16  such  columns.  Then  whatever 
pressure  is  exerted  on  the  mercury  by  the  water  in  the  small  arm  is 
transmitted  by  the  mercury  to  each  of  the  16  columns,  so  that  each 
column  receives  an  upward  pressure,  or  a  supporting  force  equal  to 
the  weight  of  the  water  in  the  small  arm.  This  method  of  transmit- 


Fig.  43. 


Fig.  44. 


TRANSMISSION   OF   EXTERNAL   PRESSURE. 


49 


ting  pressure  is  peculiar  to  fluids.  With  solids  it  is  quite  different. 
If  the  mercury  in  our  experiment  were  a  solid  body,  it  would  require 
equal  masses  of  water  placed  upon  the  two  extremities  to  counter- 
balance each  other. 

Experiment  44.  —  Support  the  seven-in-one  apparatus  with  the 
open  end  upward,  force  the  piston  in,  and  place  on  it  a  block  of  wood 
A  (Fig.  45),  and  on  the  block  a  heavy  weight  (or  let  a  small  child 
stand  on  the  block).  Attach  one  end  of  the 
rubber  tube  B  (12  feet  long)  to  the  apparatus, 
and  insert  a  tunnel  C  in  the  other  end  of  the 
tube.  Raise  the  latter  end  as  high  as  practi- 
cable, and  pour  water  into  the  tube.  Explain 
how  the  few  ounces  of  water  standing  in  the 
tube  can  exert  a  pressure  of  many  pounds  on 
the  piston,  and  cause  it  to  rise  together  with 
the  burden  that  is  on  it. 


Fig.  45. 


Fig.  46. 


Experiment  45.  —  Remove  the  water  from  the  apparatus,  place  on 
the  piston  a  16-pound  weight,  and  blow  (Fig.  48)  from  the  lungs  into 
the  apparatus.  Notwithstanding  that  the  actual  pushing  force  ex- 
erted through  the  tube  by  the  lungs  does  not  probably  exceed  an 
ounce,  the  slight  increase  of  pressure  caused  thereby  when  exerted 
upon  the  (about)  26  square  inches  of  surface  of  the  piston  causes  it  to 
rise  together  with  its  burden. 

A  pressure  exerted  on  a  given  area  of  a  fluid  enclosed 
in  a  vessel  is  transmitted  to  every  equal  area  of  the  inte- 
rior of  the  vessel;  and  the  whole  pressure  that  may  be 
exerted  upon  the  vessel  may  be  increased  in  proportion  as 
the  area  of  the  part  subjected  to  external  pressure  is  de- 
creased. 


50 


DYNAMICS   OF  FLUIDS. 


46.  Hydrostatic  Press.  —  This  principle  has  an  im- 
portant practical  application  in  the  hydrostatic  press. 
You  see  two  pistons  t  and  s  (Fig.  47).  The  area  of 
the  lower  surface  of  t  is  (say)  one  hundred  times  that  of 

the  lower  surface  of 
s.  As  the  piston  s  is 
raised  and  depressed, 
water  is  pumped  up 
from  the  cistern  A, 
forced  into  the  cylin- 
der a?,  and  exerts  a 
total  upward  pressure 
against  the  piston  t  one 
hundred  times  greater 
than  the  downward 
pressure  exerted  upon 
s.  Thus,  if  a  pressure 
Flg*  47'  of  one  hundred  pounds 

is  applied  at  8,  the  cotton  bales  will  be  subjected  to  a 
pressure  of  five  tons. 

The  pressure  that  may  be  exerted  by  these  presses  is  enormous.  The 
hand  of  a  child  can  break  a  strong  iron  bar.  But  observe  that,  although 
the  pressure  exerted  is  very  great,  the  upward  movement  of  the  piston  t  is 
very  slow.  In  order  that  the  piston  t  may  rise  1  inch,  the  piston  s  must  de- 
scend 100  inches.  The  disadvantage  arising  from  slowness  of  operation  is 
little  thought  of,  however,  when  we  consider  the  great  advantage  accruing 
from  the  fact  that  one  man  can  produce  as  great  a  pressure  with  the  press 
as  a  hundred  men  can  exert  without  it. 

The  press  is  used  for  compressing  cotton,  hay,  etc.,  into  bales,  and  for 
extracting  oil  from  seeds.  The  modern  engineer  finds  it  a  most  efficient 
machine,  whenever  great  weights  are  to  be  moved  through  short  distances, 
as  in  launching  ships, 


PRESSURE  EXERTED   BY  LIQUIDS. 


51 


Section  VII. 

PRESSURE  EXERTED  BY  LIQUIDS  DUE  TO  THEIR  OWN 
WEIGHT. 

47.   Pressure   Dependent  on  Depth,  but   Independ- 
ent of  the  Quantity  and  Shape  of  a  Body  of  Liquid.  — 

Having  considered  the  transmission  of  external  pressure  ap- 
plied to  any  portion  of  a  liquid,  we  proceed  to  examine  the 
effects  of  pressure  due  to  the  weight  of  liquids  themselves. 


Fig.  49. 


Fig.  50. 


Fig.  51. 


Experiment  46.  —  A  and  B  (Fig.  48)  are  two  bottomless  vessels 
which  can  be  alternately  screwed  to  a  supporting  ring  C  (Fig.  49).  The 
ring  is  itself  fastened  by  means  of  a  clamp  to  the  rim  of  a  wooden  water- 
pail.  A  circular  disk  of  metal,  D,  is  supported  by  a  rod  connected  with 
one  arm  of  the  balance-beam  E.  When  the  weight  F  is  applied  to  the 
other  arm  of  the  beam,  the  disk  D  is  drawn  up  against  the  ring  so  as 
to  supply  a  bottom  for  the  vessel  above.  Take  first  the  vessel  A, 
screw  it  to  the  ring,  and  apply  the  weight  to  the  beam  as  in  Figure  50. 
Pour  water  slowly  into  the  vessel,  moving  the  index  a  up  the  rod  so 


52 


DYNAMICS   OF   FLUIDS. 


as  to  keep  it  just  at  the  surface  of  the  water,  until  the  downward 
pressure  of  the  water  upon  the  bottom  tilts  the  beam,  and  pushes  the 
bottom  down  from  the  ring,  and  allows  some  of  the  water  to  fall  into 
the  pail.  Remove  vessel  A,  and  attach  B  to  the  ring  as  in  Figure  51. 
Pour  water  as  before  into  vessel  B ;  when  the  surface  of  the  water 
reaches  the  index  a,  the  bottom  is  forced  off  as  before.  That  is,  at 
the  same  depth,  though  the  quantity  of  water  and  the  shape  of  the  vessel  be 
different,  the  pressure  upon  the  bottom  of  a  vessel  is  the  same,  provided  the 
bottom  is  of  the  same  area. 

48.  Methods  of  Calculating  Liquid  Pressure.  —  Conceive 
of  a  square  prism  of  water  (Fig.  51a)  in  the  midst  of  a  body  of  water,  its 

upper  surface  coinciding  with 
the  free  surface  of  the  liquid. 
Let  the  prism  be  4  cm  deep  and 
lcm  square  at  the  end  ;  then 
the  area  of  one  of  its  ends  is 
licm?  anci  the  volume  of  the 
prism  is  4  cc.  Now  the  weight 
-  of  4CC  of  water  is  4s,  hence  this 
prism  must  exert  a  downward 
pressure  of  4e  upon  an  area  of 
1  <icin.  But  at  the  same  depth 
the  pressure  in  all  directions 
is  the  same,  hence,  generally, 
the  pressure  at  any  depth  in 
water  may  be  taken  approxi- 
mately as  one  gram  per  square 
centimeter  for  each  centimeter 
of  depth  (=0=  l,000k  per  qm 
for  each  meter  of  depth;  or, 
Fig.  5la.  since  the  weight  of  water  is 

about  62.3  Ibs.  per  cu.  ft.,  the 

pressure  is  62.3  Ibs.  per  square  foot  for  each  foot  of  depth).  In  any  other 
liquid,  to  determine  the  pressure  at  any  depth  the  water  pressure  at  the 
given  depth  must  be  multiplied  by  the  specific  gravity  of  the  liquid. 

The  conclusions  arrived  at  may  be  summarized  as  follows :  The 
pressure  due  to  gravitation  on  any  portion  of  the  bottom  of  a  vessel  contain- 
ing a  liquid  is  equal  to  the  weight  of  a  column  of  the  same  liquid  whose 
base  is  the  area  of  that  portion  of  the  bottom  pressed  upon,  and  whose  hight 
is  the  greatest  depth  of  the  water  in  the  vessel. 


PRESSURE    EXERTED    BY    LIQUIDS.  53 

Evidently  the  lateral  pressure  at  any  point  of  the  side  of  a  vessel 
depends  upon  the  depth  of  that  point ;  and,  as  depth  at  different  points 
of  a  side  varies,  hence,  to  find  the  pressure  upon  any  portion  of  a  side  of  a 
vessel,  we  find  the  weight  of  a  column  of  liquid  whose  base  is  the  area  of 
that  portion  of  the  side,  and  whose  hight  is  the  average  depth  of  that  portion. 

49.  The  Surface  of  a  Liquid  at  Best  is  Level.  —  This 
fact  is  commonly  expressed  thus:  "Water  always  seeks 
its  lowest  level."  In  accordance  with  this  principle,  water 
flows  down  an  inclined  plane,  and  will  not  remain  heaped 
up.  An  illustration  of  the  application  of  this  principle,  on 
a  large  scale,  is  found  in  the  method  of  supplying  cities 
with  water.  Figure  52  represents  a  modern  aqueduct, 
through  which  water  is  conveyed  from  an  elevated  pond 
or  river  a,  beneath  a  river  6,  over  a  hill  <?,  through  a  valley 


Fig.  52. 

d,  to  a  reservoir  0,  in  a  city,  from  which  water  is  distribu- 
ted by  service-pipes  to  the  dwellings.  The  pipe  is  tapped 
at  different  points,  and  fountains  at  these  points  would 
rise  to  the  level  of  the  water  in  the  pond,  but  for  the  re- 
sistance of  the  air,  friction  in  the  pipes,  and  the  check 
which  the  ascending  steam  receives  from  the  falling  drops. 
Where  should  the  pipes  be  made  stronger,  on  a  hill 
or  in  a  valley?  Where  will  water  issue  from  faucets 
with  greater  force,  in  a  chamber  or  in  a  basement?  How 
high  may  water  be  drawn  from  the  pipe  in  the  house  f? 


54 


DYNAMICS   OF  FLUIDS. 


Section  VIII. 

THE   SIPHON. 

5O.    Construction  and  Operation  of  the  Siphon.  —  A 

siphon  is  an  instrument  used  for  transferring  a  liquid  from 
one  vessel  to  another  through  the  agency  of  atmospheric 
pressure.  It  consists  of  a  tube  of  any  material  (rubber  is 
often  most  convenient)  bent  into  a  shape  somewhat  like 
the  letter  U.  To  set  it  in  operation,  fill  the 
tube  with  a  liquid,  stop  each  end  with  a 
finger  or  cork,  place  it  in  the  position  rep- 
resented in  Figure  53,  remove  the  stoppers 
and  the  liquid  will  all  flow  out  at  the  orifice 
o.  Why?  The  upward  pressure  of  the  at- 
mosphere against  the  liquid  in  the  tube  is 
the  same  at  both  ends ;  hence  these  two 
forces  are  in  equilibrium.  But  the  weight 
of  the  column  of  liquid  db  is  greater  than 
the  weight  of  the  column  dc\  hence  equilibrium  is  de- 
stroyed and  the  movement  is  in  the  direction  of  the  greater 
(i.e.  the  unbalanced)  force.  The  unbalanced  force  which 
causes  the  flow  is  equal  to  the  weight  of  the  column  eb. 

If  one  end  of  the  tube  filled  with  liquid  is  immersed  in 
a  liquid  in  some  vessel,  as  in  A,  Figure  54,  and  the  other 
end  is  brought  below  the  surface  of  the  liquid  in  the  vessel 
and  the  stoppers  are  removed,  the  liquid  in  the  vessel  will 
flow  out  through  the  tube  until  the  distance  eb  becomes 
zero. 


Fig.  53. 


If  one  .of  the  vessels  is  raised  a  little,  as  in  C,  the  liquid  will  flow  from 
the  raised  vessel,  till  the  surfaces  in  the  two  vessels  are  on  the  same  level 


THE   SIPHON. 


55 


The  remaining  diagrams  in  this  cut  represent  some  of  the  great  variety  of 
uses  to  which  the  siphon  may  be  put.  D,  E,  and  F  are  different  forms  of 
siphon  fountains.  In  D,  the  siphon  tube  is  filled  by  blowing  in  the  tube  /. 
Explain  the  remainder  of  the  operation.  A  siphon  of  the  form  G  is  always 
ready  for  use.  It  is  only  necessary  to  dip  one  end  into  the  liquid  to  be 


54. 


transferred.  Why  does  the  liquid  not  flow  out  of  this  tube  in  its  present 
condition"?  H  illustrates  the  method  by  which  a  heavy  liquid  may  be 
removed  from  beneath  a  lighter  liquid..  By  means  of  a  siphon  a  liquid 
may  be  removed  from  a  vessel  in  a  clear  state,  without  disturbing  sediment 


56 


DYNAMICS   OF  FLUIDS. 


at  the  bottom.  I  is  a  Tantalus  Cup.  A  liquid  will  not  flow  from  this  cup 
till  the  top  of  the  bend  of  the  tube  is  covered.  It  will  then  continue  to  flow 
as  long  as  the  end  of  the  tube  is  in  the  liquid.  The  cup  g  (Fig.  34,  page 
42)  is  a  Tantalus  cup.  The  siphon  J  may  be  filled  with  a  liquid  that  is 
not  safe  or  pleasant  to  handle,  by  placing  the  end  j  in  the  liquid,  stopping 
the  end  k,  and  sucking  the  air  out  at  the  end  /  till  the  lower  end  is  filled 
with  the  liquid. 

Gases  heavier  than  air  may  be  siphoned  like  liquids.  Vessel  o  contains 
carbonic-acid  gas.  As  the  gas  is  siphoned  into  the  vessel  p,  it  extinguishes 
a  candle-flame.  Gases  lighter  than  air  are  siphoned  by  inverting  both  the 
vessels  and  the  siphon. 


Section  IX. 


BUOYANT   FORCE   OF   FLUIDS. 

51.    Origin  of  Buoyancy. 

Experiment  47.  —  Gradually  lower  a  large  stone,  by  a  string  tied 
to  it,  into  a  bucket  of  water,  and  notice  that 
its  weight  gradually  becomes  less  till  it  is  com- 
pletely submerged.  Slowly  raise  it  out  of  the 
water,  and  note  the  change  in  weight  as  it  emerges 
from  the  water.  Suspend  the  stone  from  a  spring 
balance,  weigh  it  in  air  and  then  in  water,  and 
ascertain  its  loss  of  weight  in  the  latter. 

It  seems  as  if  something  in  the  fluid, 
underneath  the  articles  submerged,  were 
pressing  up  against  them.  A  moment's  re- 
flection will  make  the  explanation  of  this 
phenomenon  apparent.  We  have  learned  (1)  that  pressure 
at  any  given  point  in  a  body  of  fluid  is  equal  in  all  direc- 
tions. (2)  That  pressure  in  liquids  increases  as  the 


Fig.  55. 


BUOYANT  FORCE  OF    FLUIDS. 


57 


depth.  Consequently,  the  downward  pressure  on  the  top 
(i.e.  the  place  of  least  depth)  of  a  body  immersed  in  a 
fluid,  as  dcba  (Fig.  55),  must  be  less  than  the  upward 
pressure  against  the  bottom;  hence,  there  is  an  unbal- 
anced force  acting  upward,  which  tends  to  neutralize  to 
some  extent  the  weight  or  gravity  of  the  body.  This 
unbalanced  force  is  called  the  buoyant  force  of  fluids. 
That  there  is  equilibrium  between  the  pressures  on  the 
sides  of  a  body  immersed  is  shown  by  the  fact  that  there 
is  no  tendency  to  move  laterally. 

52.    Magnitude  of  the  Buoyant  Force. 

Experiment  48.  —  Suspend  from  one  arm  of  a  balance  beam  a 
cylindrical  bucket  A  (Fig.  56),  and  from  the  bucket  a  solid  cylinder 
whose  volume  is  exactly  equal  to  the 
capacity  of  the  bucket;  in  other  words, 
the  latter  would  just  fill  the  former. 
Counterpoise  the  bucket  and  cylinder 
with  weights. 

Place  beneath  the  cylinder  a  tumbler  of 
water,  and  raise  the  tumbler  until  the  cyl- 
inder is  completely  submerged.  The 
buoyant  force  of  the  water  destroys  the 
equilibrium.  Pour  water  into  the  bucket ; 
when  it  becomes  just  even  full,  the  equi- 
librium is  restored. 

Now  it  is  evident  that  the  cylinder 
immersed  in  the  water  displaces  its  own 
volume  of  water,  or  just  as  much  water 
as  fills  the  bucket.  But  the  bucket  full 
of  water  is  just  sufficient  to  restore  the  weight  lost  by  the  submersion 
of  the  cylinder.  Hence,  a  solid  immersed  in  a  liquid  is  buoyed  up  with  a 
force  equal  to  (i.e.  its  apparent  loss  in  weight  is)  the  weight  of  the 
liquid  it  displaces. 

Experiment  49.  —  The  last  statement  may  be  verified  in  another 
way  with  apparatus  like  that  shown  in  Figure  57.  Fill  the  vessel  A 
till  the  liquid  overflows  at  E.  After  the  overflow  ceases,  place  a  ves- 


Fig.  56. 


58 


DYNAMICS   OF  FLUIDS. 


Bel  c  under  the  nozzle.    Suspend  a  stone  from  the  balance-beam  B, 
and  weigh  it  in  air,  and  then   carefully  lower  it  into  the  liquid, 

when  some  of  the  liquid 
will  flow  into  the  vessel  c. 
The  vessel  c  having  been 
weighed  when  empty,  weigh 
it  again  with  its  liquid 
contents,  ^nd  it  will  be 
found  that  its  increase  in 
weight  is  just  equal  to  the 
loss  of  weight  of  the  stone. 
Experiment  50.  —  Next 
suspend  a  block  of  wood 
that  will  float  in  the  liquid, 
and  weigh  it  in  air.  Then 
float  it  upon  the  liquid,  and 
weigh  the  liquid  displaced  as 
before,  and  it  will  be  found 
that  the  weight  of  the  liquid 
Fig.  67.  displaced  is  just  equal  to  the 

weight  of  the  block  in  air. 

Hence,  a  floating  body  displaces  its  own  weight  of  liquid  ; 
in  other  words,  a  floating  body  will  sink  till  it  displaces  an 
equal  weight  of  the  liquid,  or  till  it  reaches  a  depth  where 
the  buoyant  force  is  equal  to  its  own  weight. 


Experiment  51.  —  Place  a  baroscope  (Fig.  58), 
consisting  of  a  scale-beam,  a  small  weight,  and  a 
hollow  brass  sphere,  under  the  receiver  of  an  air- 
pump,  and  exhaust  the  air.  In  the  air  the  weight 
and  sphere  balance  each  other;  but  when  the 
air  is  removed,  the  sphere  sinks,  showing  that  in 
reality  it  is  heavier  than  the  weight.  In  the  air 
each  is  buoyed  up  by  the  weight  of  the  air  it  dis- 
places ;  but  as  the  sphere  displaces  more  air,  it  is 
buoyed  up  more.  Consequently,  when  the  buoyant 
force  is  withdrawn  from  both,  their  equilibrium 
is  destroyed. 


Fig.  68. 


DENSITY  AND   SPECIFIC   GRAVITY. 


59 


We  see  from  this  experiment  that  bodies  weigh  less  in 
air  than  in  a  vacuum,  and  that  we  never  ascertain  the  true 
weight  of  a  body,  except  when  weighed  in  a  vacuum. 

The  density  of  the  atmosphere  is  greatest  at  the  surface 
of  the  earth.  A  body  free  to  move  cannot  displace  more 
than  its  own  weight  of  a  fluid ;  therefore  a  balloon,  which 
is  a  large  bag  filled  with  a  gas  about  fourteen  times  lighter 
than  air  at  the  sea-level,  will  rise  till  the  balloon,  plus  the 
weight  of  the  car  and  cargo,  equals  the  weight  of  the  air 
displaced. 

Figure  59  represents  a  water-tank  in  common  use  in  our  houses.  Water 
enters  it  from  the  main 
until  nearly  full,  when  it 
reaches  the  hollow  metallic 
ball  A,  and  raises  it  by  its 
buoyant  force  and  closes  a 
valve  in  the  main  pipe,  and 
thus  prevents  an  overflow. 
An  overflow  is  still  further 
prevented  by  the  waste 
pipe  and  another  "  ball 
tap,"  B,  which  opens  at 
a  suitable  time  another 
passage  for  the  escape  of 
water. 

Pig.  39. 


Section  X. 

DENSITY,  SPECIFIC   DENSITY,  AND   SPECIFIC    GRAVITY. 

53.  Terms  Defined.  —  The  density  of  a  substance  at 
any  temperature  is  the  mass  per  unit  of  volume  of  the 
substance  at  that  temperature.  Thus,  the  density  of  water 


60  DYNAMICS    OF    FLUIDS. 

at  4°  C.  is  one  gram  per  cubic  centimeter,  and  the  density 
of  cast  iron  at  the  same  temperature  is  about  7.12  grams 
per  cubic  centimeter.  The  mean  density  of  a  body  is 
found  by  dividing  its  mass  by  its  volume. 

The  specific  density  of  a  substance  is  the  number  which 
expresses  how  many  times  denser  the  substance  is  than  some 
standard  substance.  The  specific  gravity  of  a  substance  is 
the  ratio  of  the  weight  of  a  body  of  that  substance  to  the 
weight  of  an  equal  volume  of  some  standard.  The  standard 
adopted  for  solids  and  liquids  is  distilled  water  at  some 
definite  temperature  (in  scientific  work  at  4°  C.).  Evi- 
dently the  number  which  expresses  the  specific  density  of 
a  substance  and  the  number  which  expresses  the  specific 
gravity  of  the  same  substance  are  identical,  and  both  are 
abstract  numbers. 

54.  Formulas  for  Specific  Density  and  Specific  Grav- 
ity.—  Let  D  represent  the  density  of  any  given  substance 
(e.g.  lead),  and  D'  the  density  of  water,  and  let  G  and  Gf 
represent  respectively  the  weights  of  equal  volumes  of  the 
same  substances;  then 

Density  of  given  substance  _  D ^     -^ 

Density  of  water  "  D'  " 

Weight  of  a  given  volume  of  the  substance  _  G_  _  o    ^ 
Weight  of  equal  volume  of  water       ~  G;  ~ 

The  Sp.  D.  of  lead  =  — f  =  —  =  11.5.  The  Sp.  G.  of 
lead  =~=-iM  =  11.5.  Hence  Sp.  D.  and  Sp.  G.  are 

numerically  equal.  In  the  same  way  ratios  may  be  found  for 
other  substances  and  recorded  in  a  table ;  such  a  table  ex- 
hibits both  the  specific  densities  and  the  specific  gravities 
of  the  substances.  See  Appendix  B. 


SPECIFIC  GRAVITY  AND  SPECIFIC  DENSITY. 


61 


Section  XI. 

EXPERIMENTAL  METHODS   OF   FINDING  THE  SPECIFIC 
DENSITY   AND  SPECIFIC  GRAVITY   OF  BODIES. 

55.   Solids. 

Experiment  52.  —  From  a  hook  beneath  a  scale-pan  (Fig.  60) 
suspend  by  a  fine  thread  a  small  specimen  of  a  substance  whose 
specific  gravity  is  to  be  found,  and  weigh  it,  while  dry,  in  the  air.  Then 
immerse  the  body  in  a  tumbler  of  water  (do  not  allow  it  to  touch  the 
tumbler,  and  see  that  it  is  completely  submerged),  and  weigh  it  in 
water.  The  loss  of  weight  in  water  is  evidently  G ',  i.e.  the  weight 
of  the  water  displaced  by  the  body ;  or,  in  other  words,  the  weight 
of  a  body  of  water  having  the  same  volume  as  that  of  the  specimen. 
Apply  the  formula  (2)  for  finding  the  specific  gravity. 


Fig.  60. 


Fig.  61. 


Experiment  53.  —  Take  a  piece  of  sheet  lead  one  inch  long  and 
one-half  inch  wide,  weigh  it  in  air  and  then  in  water,  and  find  its  loss 
of  weight  in  water.  [It  will  not  be  necessary  to  repeat  this  part  of 
the  operation  in  future  experiments.]  Weigh  in  air  a  piece  of  cork 
or  other  substance  that  floats  in  water,  then  fold  the  lead-sinker,  and 
place  it  astride  the  string  just  above  the  specimen,  completely  immerse 
both,  and  find  their  combined  weight  in  water.  Subtract  their  com- 
bined weight  in  water  from  the  sum  of  the  weights  of  both  in  air ; 
this  gives  the  weight  of  water  displaced  by  both.  Subtract  from  this 


62 


DYNAMICS   OF   FLUIDS. 


the  weight  lost  by  the  lead  alone,  and  the  remainder  is  G' ;  i.e.  the 
weight  of  water  displaced  by  the  cork.    Apply  formula  (2),  as  before. 

56.    Liquids. 

Experiment  54.  —  Take  a  specific-gravity  bottle  that  holds  when 
filled  a  certain  (round)  number  of  grams  of  water,  e.g.  100s,  200&,  etc. 
Fill  the  bottle  with  the  liquid  whose  specific  gravity  is  sought.  Place 
it  on  a  scale-pan  (Fig.  61),  and  on  the  other  scale-pan  place  a  piece  of 
metal  a,  which  is  an  exact  counterpoise  for  the  bottle  when  empty. 
On  the  same  pan  place  weights  b,  until  there  is  equilibrium.  The 
weights  placed  in  this  pan  represent  the  weight  G  of  the  liquid  in  the 
bottle.  Apply  formula  (2).  The  G'  (i.e.  the  100s,  200s,  etc.)  is  the 
same  in  every  experiment,  and  is  usually  etched  on  the  bottle. 

Experiment  55.  —  Take  a  pebble  stone  (e.g.  quartz)  about  the 
size  of  a  large  chestnut ;  find  its  loss  of  weight  (i.e.  G')  in  water ;  find 
its  loss  of  weight  (i.e.  G)  in  the  given  liquid.  Apply  formula  (2). 

Prepare  blanks,  and  tabulate  the  results  of  the  experiments  above 
as  follows :  — 


NAME  OF  SUBSTANCE. 

G  in 

Grams. 

G'  in 
Grams. 

Sp.  G. 
or 
Sp.  D. 

E. 

Lead        .... 

7.2 

.66 

10.9 

0.45 

When  the  result  obtained  differs  from  that  given  in  the  table  of 
specific  gravities  (see  Appendix  B),  the  difference  is  recorded  in  the 
column  of  errors  (e).  The  results  recorded  in  the  column  of  errors 
are  not  necessarily  real  errors ;  they  may  indicate  the  degree  of  im- 
purity, or  some  peculiar  physical  condition,  of  the  specimen  tested. 

57.  Hydrometers,  —  If  a  wooden,  an  iron,  and  a  lead 
ball  are  placed  in  a  vessel  containing  mercury  (Fig.  62), 


SPECIFIC   GRAVITY  AND   SPECIFIC   DENSITY. 


63 


they  will  float  on  the  mercury  at  different  depths,  accord- 
ing to  their  relative  densities.  Ice  floats,  in  water  with 
TVA>  in  mercury  with  yf-j^,  of  its  bulk  submerged.  Hence 
the  Sp.  D.  of  mercury  is  918 -f- 68  =  about  13.5. 

We  see,  then,  that  the  densities  of  liquids  may  be  com- 
pared by  seeing  to  what  depths  bodies  floating  in  them 
will  sink.  An  instrument  (A,  Fig.  63) called  a  hydrometer 1 
is  constructed  on  this  principle.  It  consists  of  a  glass 
tube  with  one  or  more  bulbs  blown  in  it,  loaded  at  one 
end  with  shot  or  mercury  to  keep  it  in  a  vertical  position 
when  placed  in  a  liquid.  It  has  a  scale  of  specific  densities 
on  the  stem,  so  that  the  experimenter  has  only  to  place  it 
in  the  liquid  to  be  tested,  and  read  its  specific  density  or 
specific  gravity  at  that  point,  B,  of  the  stem  which  is  at 
the  surface  of  the  liquid.  , 


Fig.  62. 


58.   Miscellaneous  Experiments. 

Experiment  56. — Find  the  cubical  contents  of  an  irregular  shaped 
body,  e.g.  a  stone.     Find  its  loss  of  weight  in  water.     Remember  that 
the  loss  of  weight  is  precisely  the  weight  of  the  water  it  displaces,  and 
that  the  volume  of  one  gram  of  water  is  one  cubic  centimeter. 
1  Densimeter  is  a  more  suitable  name  for  this  instrument. 


64  DYNAMICS   OF  FLUIDS. 

Experiment  57.  —  Find  the  capacity  of  a  test-tube,  or  an  irregular 
shaped  cavity  in  any  body.  Weigh  the  body ;  then  fill  the  cavity  with 
water,  and  weigh  again.  As  many  grains  as  its  weight  is  increased,  so 
many  cubic  centimeters  is  the  capacity  of  the  cavity. 

Experiment  58.  —  A  fresh  egg  sinks  in  water.  See  if  by  dissolv- 
ing table  salt  in  the  water  it  can  be  made  to  float.  How  does  salt 
affect  the  density  of  the  water  ? 

Experiment  59.  —  Float  a  sensitive  hydrometer  in  water  at  about 
60°  F.  (15°  C.),  and  in  other  water  at  about  180°  F.  (82°  C.).  Which 
water  is  denser  ? 

EXERCISES. 

1.  In  which  does  a  liquid  stand  higher,  in  the  snout  of  a  coffee-pot 
or  in  the  main  body?    On  which  does  this  show  that  pressure  depends, 
on  quantity  or  depth  of  liquid  ? 

2.  The  areas  of  the  bottoms  of  vessels  A,  B,  and  C  (Fig.  64)  are  equal. 
The  vessels  have  the  same  depth,  and  are  filled  with  water.    Which 
vessel  contains  the  more  water  ?    On  the  bottom  of  which  vessel  is  the 
pressure  equal  to  the  weight  of  the  water  which  it  contains  ?    How 
does  the  pressure  upon  the  bottom  of  vessel  B  compare  with  the 
weight  of  the  water  in  it? 


Fig.  64. 

3.  A  cubic  foot  of  water  weighs  about  62. 5  pounds  or  1,000  ounces. 
Suppose  that  the  area  of  the  bottom  of  each  vessel  is  50  square  inches 
and  the  depth  is  10  inches  ;  what  is  the  pressure  on  the  bottom  of 
each? 

4.  Suppose  that  the  vessel  A  is  a  cubical  vessel  of  10  in.  side  ; 
what  is  the  pressure  against  one  of  its  vertical  sides  ? 

5.  Suppose  that  vessel  A  were  tightly  covered,  and  that  a  tube  10 
feet  long  were  passed  through  a  perforation  in  the  cover  so  that  the 
end  just  touches  the  upper  surface  of  the  water  in  the  vessel ;  then 


SPECIFIC  GRAVITY  AND  SPECIFIC  DENSITY. 


65 


suppose  the  tube  to  be  filled  with  water.     What  additional  pressure 
will  each  side  of  the  cube  sustain  ? 

6.  Suppose  that  the  area  of  the  end  of  the  large  piston  of  a  hydro- 
static press  is  100  square  inches ;  what  should  be  the  area  of  the  end 
of  the  small  piston  that  a  force  of  100  pounds  applied  to  it  may  produce 
a  pressure  of  2  tons  ? 

7.  A  solid  body  weighs  10  pounds  in  air  and  6  pounds  in  water,    (a) 
What  is  the  weight  of  an  equal  bulk  of  water  ?     (5)  What  is  its  specific 
gravity  ?      (c)   What  is  the  volume  of  the  body  ?      (d)   What  is  its 
density  ? 

8.  A  thousand-grain    specific-gravity  bottle  filled  with  sea-water 
requires  in  addition  to  the  counterpoise  of  the  bottle  1,026  grains  to 
balance  it.     (a)  What  is  the  specific  gravity  of  sea-water  ?     (&)  What 
is  the  quantity  of  salt,  etc.,  dissolved  in  1,000  grains  of  sea-water? 

9.  A  piece  of  cork  floating  on  water  displaces  2  pounds  of  water. 
What  is  the  weight  of  the  cork  ? 

10.  In  which  would  a  hydrometer  sink  farther,  in  milk  or  water? 

11.  What  metals  will  float  in  mercury? 

12.  (a)  Which  has  the  greater  specific  gravity,  water  at  10°  C.  or 
water  at  20°  C.?    (5)  If  water  at  the  bottom  of  a  vessel  could  be 
raised  by  application  of  heat  to  20  °  C.  while  the  water  near  the  upper 
surface  has  a  temperature  of  10°  C.,  what  would  happen? 

13.  A  block  of  wood  weighs  550  grams ;   when  a  certain  irregular- 
shaped   cavity  is  fi)led  with  mercury  the  block  weighs   570  grams. 
What  is  the  capacity  or  cubical  contents  of  the  cavity? 

14.  In  which  is  it  easier  for  a  person  to  float,  in  fresh  water  or  in 
sea-water?    Why? 

15.  Figure  65  represents  a  beaker  graduated 
in  cubic  centimeters.     Suppose  that  when  water 
stands  in  the  graduate  at  50CC,  a  pebble  stone  is 
dropped  into  the  water,  and  the  water  rises  to 
75°°.      (a)  What  is  the   volume  of    the   stone? 
(&)  How  much  less  does  the  stone  weigh  in  water 
than  in  air?     (c)  What  is  the  weight  of  an  equal 
volume  of  water  ? 

16.  If  a  piece  of  cork  is  floated  on  water  in 
a,  graduate,  and  displaces  (i.e.  causes  the  water 
to  rise)  7CC,  what  is  the  weight  of  the  cork  ? 


66  DYNAMICS   OF   FLUIDS. 

17.  If  a  piece  of  lead  (sp.  g.  11.35)  is  dropped  into  a  graduate  and 
displaces  12CC  of  water,  what  does  the  lead  weigh?     (a)  How  would 
you  measure  out  50  grams  of  water  in  a  graduate  ?     (6)  How  would 
you  measure  out  the  same  weight  of  alcohol  (sp.  g.  0.8)  ?    (c)  How  the 
same  weight  of  sulphuric  acid  (sp.  g.  1.84)? 

18.  What  is  the  density  of  gold?  silver?  milk?  alcohol? 

19.  When  the  barometer  stands  at  30  inches,  how  high  can  alcohol 
be  raised  by  a  perfect  lifting-pump  ? 

20.  A  measuring  glass  graduated   in  cubic  centimeters  contains 
water.     An  empty  bottle  floats  on  the  water,  and  the  surface  of  the 
water  stands  at  50CC.     If  10s  of  lead  shot  are  placed  in  the  bottle, 
where  will  the  surface  of  the  water  stand? 

21.  What  mass  of  alcohol  can  be  put  into  a  vessel  whose  capacity  is 
1  liter  ? 

22.  On  what  two  things  does  the  weight  of  a  body  depend  ? 

23.  (a)  Can  you  suck  air  out  of  a  bottle  V     (6)  Can  you  suck  water 
out  of  a  bottle  ?    Explain. 

24.  (a)  What  bodies  have  neither  volume  nor  shape  ?     (6)  What 
have  volume,  but  not  shape?    (c)  What  have  both  volume  and  shape? 

25.  When  the  volume  of  a  body  of  gas  diminishes,  is  it  due  to  con- 
traction or  compression,  i.e.  to  internal  or  external  forces  ? 

26.  What  is  the  hight  of  the  barometer  column  when  the  atmos- 
pheric pressure  is  10  grams  per  square  centimeter  ? 

27.  A  barometer  in  a  diving-bell  (-page  3)  stands  at  96cm  when  a 
barometer  at  the  surface  of  the  earth  stands  at  76cra;  what  is  the 
depth  of   the    surface  of  water-  inside  the   bell  below  the   surface 
outside  ? 

28.  (a)  40k  of  lead  immersed  in  water  will  displace  what  volume 
of  water  ?     (6)  Will  lose  how  much  of  its  weight  ? 

29.  Find  the  sum  in  meters  of  4^m,  150cm,  8dm,  65»im,  5.6«m, 
and  4mm. 

30.  The  sp.  g.  of  hydrogen  gas  is  (page  359)  0.0693.     What  do 
you  understand  by  this  statement  ? 

31.  What  is  the  mass  of  a  liter*  of  water  at  4°C  ? 


CHAPTER   IIL 

GENERAL   DYNAMICS. 

Section  I. 

MOMENTUM   AND   ITS   RELATION   TO   FORCE. 

59.  Momentum.  —  Everyone  knows  that  the  effort  to 
stop  a  moving  body  in  a  given  time  must  depend  both 
upon  the  mass  of  the  body  and  its  velocity.     An  empty  car 
in  motion  is  much  more  easily  stopped  than  a  loaded  car, 
and  a  ball  tossed  is  a  different  affair  from  a  ball  thrown. 
We  have  an  instinctive  dread  of  the  approach  of  large 
masses  and  of  swiftly  moving  masses.     Thus  we  are  led 
to  the  consideration  of  a  quantity  called  momentum,  which 
is  t he  product  of  the  mass  of  a  body  multiplied  by  its  velocity. 
A  unit  of  momentum  is  the  momentum  of  a  unit  mass 
moving  with  unit  speed,  and  has  no  special  name.     Mo- 
mentum depends  upon  both  mass  and,  velocity ;  velocity 
is  independent  of  mass.     Momentum  =  MV. 

60.  Relation  of  Momentum  to  Force. 

Experiment  60.  —  Weights  A  and  B  of  the  Atwood  'machine 
(Fig.  66),  suspended  by  a  thread  passing  over  the  wheel  C,  are  in  equi- 
librium with  reference  to  the  force  of  gravity  ;  consequently  neither 
falls.  Raise  weight  A,  and  let  it  rest  on  the  platform  D,  as  in  Figure 
67.  The  two  weights  are  still  in  equilibrium.  Place  weight  E,  called 
a  "  rider,"  on  A.  There  is  now  an  unbalanced  force,  and  if  the  plat- 
form D  is  removed,  there  will  be  motion,  i.e.  A  and  E  will  fall,  and 
B  will  rise.  Set  the  pendulum  F  to  vibrating.  At  each  vibration  it 


68 


GENERAL   DYNAMICS. 


Fig.  66. 


causes  a  stroke  of  the  hammer  on  the  bell  G. 
At  the  instant  of  the  first  stroke  the  pendulum 
causes  the  platform  D  to  drop  so  as  to  allow 
the  weights  to  move.  When  the  weights  reach 
the  ring  H,  the  rider  is  caught  off  by  the  ring. 

Raise  and  lower  the  ring  on  the  graduated 
pillar  I,  and  ascertain  by  repeated  trials  the 
average  distance  the  weights  descend  in  the  in- 
terval between  the  first  two  strokes  of  the  bell. 

Next  substitute  for  E  a  weight  L,  double  that 
of  E.  Find  by  trial  how  far  the  weights  now 
descend  in  the  same  interval  of  time  as  before. 
It  will  be  found  that  in  the  latter  case  the 
weights  descend  nearly  twice  as  far  as  in  the 
first  case. 

Suppose  that  weights  A  and  B  are  each  30 
grams,  and  that  weights  E  and  L  are  respec- 
tively 2  grams  and  4  grams.  Now  the  force  of 
gravity  which  acts  on  weight  E  is  2  grams. 
Consequently  the  unbalanced  force  which  put 
in  motion  the  three  weights  A,  B,  and  E,  whose 
combined  weight  (disregarding  the  weight  of 
wheel  C,  which  is  also  put  in  motion)  is 
(30  +  30  +  2  =  )  62  grams,  was  2  grams.  It 
is  now  evident  why  the  descent  is  slow,  for  in- 
stead of  a  force  of  1  gram  acting  upon  each  gram 
of  matter,  as  is  usually  the  case  with  falling 
bodies,  we  have  a  force  of  only  2  grams  moving 
62  grams  of  matter;  consequently 'the  descent 
is  about  -fa  as  fast  as  that  of  falling  bodies 
generally. 

But  when  we  employed  weight  L,  we  had  a 
force  of  4  grams  moving  (30  +  30  +  4  =)  64 
grams  of  matter.  Here  the  force  is  doubled, 
and  the  distance  traversed  is  nearly  doubled; 
consequently  the  average  velocity  and  the  mo- 
mentum acquired  are  nearly  doubled.  Had  the 
masses  moved  in  the  two  cases  been  exactly  the 
same,  the  velocity  and  the  momentum  would 
have  been  exactly  doubled. 


FIRST   LAW   OF   MOTION.  69 

(1)  In  equal  intervals  of  time  change  of  momentum  is 
proportional  to  the  force  employed. 

Experiment  61.  —  Once  more  place  E  on 
A,  and  ascertain  how  far  they  will  descend 
between  the  first  and  third  strokes  of  the 
bell,  i.e.  in  double  the  time  employed  before. 
It  will  be  found  that  they  will  descend  in 
the  two  units  of  time  about  four  times  as 
far  as  during  the  first  unit  of  time.  Later 
on  it  will  be  shown  that,  in  order  to  accom- 
plish this,  the  velocity  at  the  end  of  the  sec- 
ond unit  of  time  must  be  twice  that  at  the  end 
of  the  first  unit  of  time.  If  MV  represent 
the  momentum  generated  during  the  first 
unit  of  time,  then  the  momentum  generated 
during  the  second  unit  of  time  must  be  about 
2MV. 

(2)  The  momentum  generated  "by  a 

given  force  is  proportional  to  the  time  during  which  the  force 
acts. 

Conclusions  (1)  and  (2)  are  summarized  in  the  formula 
MV=  Ft,  and  in  the  Second  Law  of  Motion,  §  63. 


Section  II. 

FIRST    LAW    OF    MOTION. 

The  relations  between  matter  and  force  are  concisely 
expressed  in  what  are  known  as  The  Three  Laws  of 
Motion  first  enunciated  by  Sir  Isaac  Newton. 

61.  First  Law  of  Motion.  —  A  body  at  rest  remains  at 
rest,  and  a  body  in  motion  moves  with  uniform  velocity  in  a 
straight  line,  unless  acted  upon  by  some  external  force. 


70  GENERAL   DYNAMICS. 

A  body  is  said  to  be  acted  upon  by  an  "external  force  " 
when  the  action  is  between  that  body  and  some  other  body 
(in  contradistinction  from  an  action  between  parts  of  the 
same  body). 

The  tendency  of  matter  to  remain  in  the  state  that  it  is 
in,  whether  it  be  rest  or  motion,  is  called  inertia;  hence 
the  First  Law  of  Motion  is  often  called  the  Law  of  Inertia. 

The  backward  motion  of  passengers  when  a  car  is  suddenly  started, 
and  their  forward  motion  when  the  car  is  suddenly  stopped,  the  difficulty 
in  starting  a  vehicle  and  the  comparative  ease  of  keeping  it  in  motion 
after  it  is  put  in  motion,  and  the  ceaseless  motion  of  the  planets,  are 
illustrations  of  inertia.  By  virtue  of  inertia  the  swiftly  flying  bullet 
pierces  a  plank. 


Section  III. 

SECOND    LAW   OF  MOTION. 

62.    Graphical  Representation  of  Motion  and  Force. 

—  If  a  person  wishes  to  describe  to  you  the  motion  of 
a  ball  struck  by  a  bat,  he  must  tell  you  three  things: 
(1)  where  it  starts,  (2)  in  what  direction  it  moves,  and 
(3)  how  far  it  goes.  These  three  essential  elements  may 

be    represented    graphically   by 
lines.     Thus,  suppose  balls  at  A 
and  D   (Fig.  68)   to  be  struck 
by  bats,  and  that  they  move  re- 
Fig,  es.  spectively   to   B   and  E  in  one 
second.     Then  the   points  A  and   D   are   their   starting- 
points  ;   the  lines  AB  and  DE  represent  the  direction  of 
their  motions,  and  the  lengths  of  the  lines  represent  the 


SECOND   LAW    OF   MOTION.  71 

distances  traversed.  In  reading,  the  direction  should  be 
indicated  by  the  order  of  the  letters,  as  AB  and  DE. 

Likewise,  the  forces  which  produce  the  motion  may  be 
represented  graphically.  For  example,  the  points  A  and 
D  may  represent  the  points  of  application  of  two  forces, 
the  lines  AB  and  DE  represent  the  direction  in  which  they 
act,  and  the  length  of  the  lines  represent  their  relative 
intensities. 

Let  a  force  whose  intensity  may  be  represented  numeri- 
cally by  8  (e.g.  8  pounds),  acting  in  the  direction  AB  (Fig. 
69),  be  applied  continuously  to 
a  ball  starting  at  A,  and  sup- 
pose this  force  capable  of  mov- 
ing it  to  B  in  one  second ;  now, 
at  the  end  of  the  second  let 
a  force  of  the  intensity  of  4, 
directed  at  right  angles  to  the 
direction  of  the  former  force, 
act  during  a  second  —  it  would  rig.  69. 

move  the  ball  to  C.  If,  however,  when  the  ball  is  at  A, 
both  of  these  forces  should  be  applied  at  the  same  time,  then 
at  the  end  of  a  second  the  ball  will  be  found  at  C.  Its 
path  will  not  be  AB  nor  AD,  bat  an 'intermediate  one, 
AC.  Still  each  force  produces  its  own  peculiar  result,  for 
neither  alone  would  carry  it  to  C,  but  both  are  required. 

63.  Second  L.aw  of  Motion.  —  Change  of  momentum  is 
in  the  direction  in  which  the  force  acts,  and  is  proportional 
to  its  intensity  and  the  time  during  which  it  acts  (see  Sec.  I). 

This  law  implies  that  an  unbalanced  force  of  the  same 
intensity,  in  the  same  time,  always  produces  exactly  the 
same  change  of  momentum,  regardless  of  the  mass  of  the 
body  on  which  it  acts,  and  regardless  of  whether  the  body  is 
in  motion  or  at  rest,  and  whether  the  force  acts  alone  or  with 
others  at  the  same  time. 


72  GENERAL  DYNAMICS. 

Section  IV. 

COMPOSITION  AND  RESOLUTION   OF   FORCES. 

64.    Composition  of  Forces.  —  It  is  evident  that  a  sin- 
gle force,  applied  in  the  direction  AC   (Fig.  69),  might 
produce    the   same  result   that   is   produced   by  the   two 
forces  represented  by  AB  and  AD.     Such  a  force  is  called 
a  resultant.    A  resultant  is  a  single  force  that  may  be  sub- 
stituted for  two  or  more  forces, 
and  produce  the  same  result 
that   the   simultaneous   action 
of  the  combined  forces  produce. 
The  several  forces  that  con- 
tribute to  produce  the  result- 
ant are  called  its  components. 
When    the    components    are 
given,  and  the  resultant  re- 
quired, the  problem  is  called 

composition  of  forces.  The  resultant  of  two  forces  acting 
simultaneously  at  an  angle  to  each  other  may  always  be 
represented  ly  a  diagonal  of  a  parallelogram,  of  which  the 
two  adjacent  sides  represent  the  components.  Thus,  the 
lines  AD  and  AB  represent  respectively  the  direction  and 
relative  intensity  of  each  component,  and  AC  represents 
the  direction  and  intensity  of  the  resultant. 

The  numerical  value  of  the  resultant  may  be  found  by 
comparing  the  length  of  the  line  AC  (Fig.  69)  with  the 
length  of  either  AB  or  AD,  whose  numerical  values  are 
known.  Thus,  AC  is  2.23  times  AD  ;  hence,  the  numer- 
ical value  of  the  resultant  AC  is  (4  X  2.23  = )  9.92. 
When  more  than  two  components  are  given,  find  the  result- 


COMPOSITION   AND   RESOLUTION   OF   FORCES.  73 

ant  of  any  two  of  them,  then  of  this  resultant  and  a  third,  and 
so  on  until  every  component  has  been  used.  Thus  in  Fig.  70, 
AC  is  the  resultant  of  AB  and  AD,  and  AF  is  the  result- 
ant of  AC  and  AE,  i.e.  of  the  three  forces  represented  by 
the  lines  AB,  AD,  and  AE.  Generally  speaking,  a  motion 
may  be  the  result  of  any  number  of  forces.  When  we  see  a 
body  in  motion,  we  cannot  determine  by  its  behavior  how 
many  forces  have  concurred  to  produce  its  motion. 

65.  Resolution  of  Forces.  —  Assume  that  a  ball  moves 
a  certain  distance  in  a  cer- 
tain direction,  AC  (Fig. 
71),  under  the  combined 
influence  of  two  forces, 
and  that  one  of  the  forces 
that  produces  this  motion 
is  represented  in  intensity 

and  direction  by  the  line  AB :  what  must  be  the  intensity 
and  direction  of  the  other  force  ?  Since  AC  is  the  result- 
ant of  two  forces  acting  at  an  angle  to  each  other,  it  is  the 
diagonal  of  a  parallelogram  of  which  AB  is  one  of  the  sides. 
From  C  draw  CD  parallel  with  and  equal  to  BA,  and  com- 
plete the  parallelogram  by  connecting  the  points  B  and  C, 
and  A  and  D.  Then,  according  to  the  principle  of  compo- 
sition of  forces,  AD  represents  the  intensity  and  direction 
of  the  force  which,  combined  with  the  force  AB,  would  move 
the  ball  from  A  to  C.  The  component  AB  being  given, 
no  other  single  force  than  AD  will  satisfy  the  question. 

Experiment  62.  —  Verify  the  preceding  propositions  in  the  follow- 
ing manner :  From  pegs  A  and  B  (Fig.  72),  in  the  frame  of  a  black- 
board, suspend  a  known  weight  W,  of  (say)  10  pounds,  by  means  of 
two  strings  connected  at  C.  In  each  of  these  strings  insert  dyna- 
mometers x  and  y.  Trace  upon  the  blackboard  short  lines  along  the 
strings  from  the  point  C,  to  indicate  the  direction  of  the  two  com- 


74  GENERAL  DYNAMICS. 

ponent  forces ;  also  trace  the  line  CD,  in  continuation  of  the  line  WC, 
to  indicate  the  direction  and  intensity  of  the  resultant.  Remove 

the  dynamometers,  extend  the 
lines  (as  Ca  and  C6),  and  on 
these  construct  a  parallelo- 
gram, from  the  extremities  of 
the  line  CD  regarded  as  a 
diagonal.  It  will  be  found 
that  10 :  number  of  pounds  in- 
dicated by  the  dynamometer 
o:::CD:Ca;  also  that  10: 
number  of  pounds  indicated 
by  the  dynamometer  y  : :  CD  : 
C6.  Again,  it  is  plain  that  a 

single  force  of  10  pounds  must  act  in  the  direction  CD  to  produce  the 
same  result  that  is  produced  by  the  two  components.  Hence,  when 
two  sides  of  a  parallelogram  represent  the  intensity  and  direction  of  two 
component  forces,  the  diagonal  represents  the  resultant.  Vary  the  problem 
by  suspending  the  strings  from  different  points,  as  E  and  F,  A  and 
F,  etc. 

An  excellent  verification  of  the  Second  Law  of  Motion 
and  the  principle  of  composition  of  forces  is  found  in  the 
fact  that  a  ball,  projected  horizontally,  will  reach  the 
ground  in  precisely  the  same  time  that  it  would  if  dropped 
from  a  state  of  rest  from  the  same  hight.  That  is,  any 
previous  motion  a  body  has  in  any  direction  does  not 
affect  the  action  of  gravity  upon  the  body. 

Experiment  63.  —  Draw  back  the  rod  d  (Fig.  73)  toward  the  left, 
and  place  the  detent-pin  c  in  one  of  the  slots.  Place  one  of  the  brass 
balls  on  the  projecting  rod,  and  in  contact  with  the  end  of  the  instru- 
ment, as  at  A.  Place  the  other  ball  in  the  short  tube  B.  Raise  the 
apparatus  to  as  great  an  elevation  as  practicable,  and  place  it  in  a 
perfectly  horizontal  position.  Release  the  detent,  and  the  rod,  pro- 
pelled by  the  elastic  force  of  the  spring  within,  will  strike  the  ball  B 
with  great  force,  projecting  it  in  a  horizontal  direction.  At  the  same 
instant  that  B  leaves  the  tube  and  is  free  to  fall,  the  ball  A  is  re- 
leased from  the  rod,  and  begins  to  fall.  The  sounds  made  on  strik- 


COMPOSITION   AND    RESOLUTION   OF  FORCES. 


75 


ing  the  floor  reach  the  ears  of  the  observer  at  the  same  instant; 
this  shows  that  both  balls  reach  the  floor  in  sensibly  the  same  time, 
and  that  the  horizontal  motion  which  one  of  the  balls  has  does  not 
affect  the  time  of  its  fall. 


Fig.  73. 

66.  Composition  of  Parallel  Forces,  —  If  the  strings 
CA  and  CB  (Fig.  72)  are  brought  nearer  to  each  other  (as 
when  suspended  from  B  and  E)  so  that  the  angle  formed 
by  them  is  diminished,  the  component  forces,  as  indicated 
by  the  dynamometers,  will  decrease,  till  the  two  forces 
become  parallel,  when  the  sum  of  the  'components  just 
equals  the  weight  W.  Hence,  (1)  two  or  more  forces 
applied  to  a  body  act  to  the  greatest  advantage  when  they 
are  parallel,  and  in  the  same  direction,  in  which  case  their 
resultant  equals  their  sum. 

On  the  other  hand,  if  the  strings  are  separated  from 
each  other,  so  as  to  increase  the  angle  formed  by  them, 
the  forces  necessary  to  support  the  weight  increase  until 
they  become  exactly  opposite  each  other,  when  the  two 
forces  neutralize  each  other,  and  none  is  exerted  in  an 
upward  direction  to  support  the  weight.  If  the  two  strings 


76  GENERAL  DYNAMICS. 

are  attached  to  opposite  sides  of  the  weight  (the  weight 
being  supported  by  a  third  string),  and  pulled  with  equal 
force,  the  weight  does  not  move.  But  if  one  is  pulled 
with  a  force  of  15  pounds,  and  the  other  with  a  force  of 
10  pounds,  the  weight  moves  in  the  direction  of  the 
greater  force ;  and  if  a  third  dynamometer  is  attached  to 
the  weight,  on  the  side  of  the  weaker  force,  it  is  found 
that  an  additional  force  of  five  pounds  must  be  applied 
to  prevent  motion.  Hence,  (2)  when  two  or  more  forces 
are  applied  to  a  body,  they  act  to  greater  disadvantage  the 
farther  their  directions  are  removed  from  one  another ;  and 
the  result  of  parallel  forces  acting  in  opposite  directions  is 
a  resultant  force  in  the  direction  of  the  greater  force,  equal 
to  their  difference. 

When  parallel  forces  are  not  applied  at  the  same  point, 
the  question  arises,  What  will  be  the  point  of  application 
of  their  resultant?  To  the  opposite  extremities  of  a  bar 

AB(Fig.74)  apply  two 
sets  of  weights,  which 
shall  be  to  each  other 
as  3  Ibs. :  1  Ib.  The 
resultant  is  a  single 
force,  applied  at  some 
Fig'  74<  point  between  A  and 

B.  To  find  this  point  it  is  only  necessary  to  find  a 
point  where  a  single  force,  applied  in  an  opposite  direc- 
tion, will  prevent  motion  resulting  from  the  parallel 
forces;  in  other  words,  to  find  a  point  where  a  support 
may  be  applied  so  that  the  whole  will  be  balanced.  That 
point  is  found  by. trial  to  be  at  the  point  C,  which  divides 
the  bar  into  two  parts  so  that  AC  :  CB  : :  1  Ib. :  3  Ibs. 
Hence,  (3)  when  two  parallel  forces  act  upon  a  body  in 
the  same  direction,  the  distances  of  their  points  of  applica- 


COMPOSITION   AND    RESOLUTION   OF   FORCES.  77 

tion  from  the  point   of  application  of  their  resultant  are 
inversely  as  their  intensities. 

The  dynamometer  E  indicates  that  a  force  equal  to  the 
sum  of  the  two  sets  of  weights  is  necessary  to  balance  the 
two  forces.  A  force  whose  effect  is  to  balance  the  effects 
of  one  or  more  forces  is  called  an  equilibrant.  The  result- 
ant of  the  two  components  is  a  single  force,  equal  to  their 
sum,  applied  at  C  in  the  direction  CD. 

67.  Moment  of  a  Force.  —  The  value  of  a  force 
to  produce  rotation  about  a  given  axis  as  C  (Fig.  75) 
is  called  its  moment 

A  fcjt  C  3ft  B 

about  that  axis.     The 


a 

0  Ibs.  ,a)  UB, 

\  \ 

n  M 


perpendicular  distance   * 
(AC  or  BC)  from  the 
fixed  point  (C)  to  the  M*  re- 

line  of  direction  in  which  the  force  acts  (AD  or  BE)  is 
called  the  leverage  or  arm.  The  moment  of  a  force  is  meas- 
ured by  the  product  of  the  number  of  units  of  force  into  the 
number  of  units  of  leverage.  For  example,  the  moment  of 
the  force  applied  at  A  is  expressed  numerically  by  the 
number  (30  x  2  =)  60. 

68.  Equilibrium  of  Moments.  —  The  moment  of  a 
force  is  said  to  be  positive  when  it  tends  to  produce  rota- 
tion in  the  direction  in  which  the  hands  of  a  clock  move, 
and  negative  when  its  tendency  is  in  the  reverse  direction. 
If  two  forces  act  at  different  points  of  a  body  which  is 
free  to  rotate  about  a  fixed  point,  they  will  produce  equi- 
librium when  their  moments  are  opposite  and  their  alge- 
braic sum  is  zero.  Thus  the  moment  of  the  force  applied 
at  A  (Fig.  75)  is  (-30  X  2) -60.  The  moment  of  the 
force  applied  at  B  in  an  opposite  direction  is  accordingly 
(+  20  X  3  =)  -f  60.  Their  algebraic  sum  is  zero,  conse- 
quently there  is  equilibrium  between  the  forces. 


78  GENERAL   DYNAMICS. 

When  more  than  two  forces  act  in  this  manner,  there 
will  be  equilibrium   if  the   sum  of  all  the  positive   mo- 
ll §*  ments  is  equal  to  the 
a\                                   b\  sum  of  all  the  nega- 

soi — ^ T — £ j ^ |3o     tive  moments.     Thus 

c\  d\  c\  f\       the  sum  of  the  posi- 

ijg  s  2%  vt     tive  moments  acting 

Fig*  76*  about  point  F  (Fig. 

76)  is  (/)  45 +  (e)25  + (a)  30  =100;    the    sum    of    the 

negative  moments  acting  about  the  same  point  is  (c)  30  + 

(<f)  40  +  (6)  30  =  100 ;    the    two   sums  being  equal,   the 

forces  are  in  equilibrium. 

69.  Mechanical  Couple. — 
Two  equal  forces  applied  to  the 
same  body  (e.g.  AB,  Fig.  77)  in 
parallel  and  opposite  directions 
not  in  the  same  line  constitute 
what  is  called  a  mechanical 
77-  couple.  The  effect  of  a  couple 

is  to  produce  rotation,  but  no  motion  of  translation.  The 
moment  of  a  couple  is  the  sum  of  the  moments  of  its  two 
components  around  the  axis  of  rotation. 


Section  V. 

THE   THIRD   LAW   OF   MOTION. 

7O.  Introductory  Experiments.  —  We  have  learned 
that  motion  cannot  originate  in  a  single  body,  but  arises 
from  mutual  action  between  two  bodies  or  two  parts  of  a 
body.  For  example,  a  man  can  lift  himself  by  pulling 


THE  THIRD   LAW   OF   MOTION. 


79 


on  a  rope  attached  to  some  other  object,  but  not  by  his 
boot-straps,  or  a  rope  attached  to  his  feet.  In  every  change 
in  regard  to  motion  there  are  always  at  least  two  bodies 

oppositely  affected. 

Experiment  64.  —  Suspend  the  deep  glass  bucket  A  (Fig.  78)  by 
means  of  a  strong  thread  two  feet  long,  so  that  the  long  projecting 
pointer  may  be  directly  over  a  dot  made  on  a 
piece  of  paper  placed  beneath ;  or  place  beneath 
another  pointer,  B,  so  that  the  two  points  shall 
just  meet.  Fill  the  bucket  with  water.   Gravity 
causes  the  water  to  flow  from  the  orifice  C ; 
A   but  the  bucket  moves  in  the  opposite  direction. 


Fig.  78. 


Fig.  79. 


Experiment  65.  —  Place  the  hollow  glass  globe  and  stand  (Fig. 
79)  under  the  receiver  of  an  air-pump,  and  exhaust  the  air.  The  air 
within  the  globe  expands,  and  escapes  from  the  small  orifices  a  and  c 
at  the  extremity  of  the  two  arms.  But  this  motion  of  the  air  is 
attended  by  an  opposite  motion  of  the  arms  and  globe,  and  a  rapid 
rotation  is  caused. 

A  man  in  a  boat  weighing  one  ton  pulls  at  one  end  of  a 
rope,  the  other  end  of  which  is  held  by  another  man,  who 


80  GENBBAL  DYNAMICS. 

weighs  twice  as  much  as  the  first  man,  in  a  boat  weighing 
two  tons :  both  boats  will  move  towards  each  other,  but 
in  opposite  directions ;  if  the  resistances  which  the  two 
boats  encounter  were  the  same,  the  lighter  boat  would 
move  twice  as  fast  as  the  heavier,  but  with  the  same 
momentum. 

If  the  boats  are  near  each  other,  and  the  men  push  each 
other's  boats  with  oars,  the  boats  will  move  in  opposite 
directions,  though  with  different  velocities,  yet  with  equal 
momenta. 

The  opposite  impulses  received  by  the  bodies  concerned 
are  usually  distinguished  by  the  terms  action  and  reaction. 
We  measure  these,  when  both  are  free  to  move,  by  the 
momenta  generated,  which  is  always  the  same  in  both 
bodies. 

71.  Third  Law  of  Motion.  —  To  every  action  there  is 
an  equal  and  opposite  reaction. 

The  application  of  this  law  is  not  always  obvious. 
Thus,  the  apple  falls  to  the  ground  in  consequence  of  the 
mutual  attraction  between  the  apple  and  the  earth.  The 
earth  does  not  appear  to  fall  toward  the  apple.  But, 
as  the  mass  of  the  earth  is  enormously  greater  than  that 
of  the  apple,  its  velocity,  for  an  equal  momentum,  is 
proportionately  less. 

EXERCISES. 

1.  (a)  Why  does  not  a  given  force,  acting  the  same  length  of  time, 
give  a  loaded  car  as  great  a  velocity  as  an  empty  car?    (6)   After 
equal  forces  have  acted  for  the  same  length  of  time  upon  both 
cars,  and  given  them  unequal  velocities,  which  will  be  the   more 
dimcult  to  stop? 

2.  (a)  The  planets  move  unceasingly ;  is  this  evidence  that  there 
are  forces  pushing  or  pulling  them  along?      (&)    None    of    their 
motions  are  in  straight  lines;  are  they  acted  upon  by  external  forces? 


THE  THIRD  LAW   OF  MOTION.  81 

• 

3.  A  certain  body  is  in  motion ;  suppose  that  all  hindrances  to 
motion  and  all  external  forces  were  withdrawn  from  it,  how  long 
would  it  move?    Why?    In  what  direction?    Why?    With  what 
kind  of  motion,  i.e.  accelerated,  retarded,  or  uniform?    Why? 

4.  Copy  upon  paper  and  find  the  resultant  of  the  components  AB 
and  AC  in  each  of  the  four  diagrams  in  Figure  80.    Also  assign  ap- 
propriate numerical  values  to  each  component,  and   find  the  corre- 
sponding numerical  value  of  each  resultant. 


Tig.  80. 

5.  Explain  how  rotating  lawn-sprinklers  are  kept  in  motion. 

6.  When  you  leap  from  the  earth,  which  receives  the  greater  mo- 
mentum, your  body  or  the  earth  ? 

7.  When  you  kick  a  door-rock,  why  does  snow  or  mud  on  your 
shoes  fly  off? 

8.  Why  cannot  a  person  propel  a  vessel  during  a  calm  by  blowing 
the  sails  with  a  big  bellows  placed  on  the  deck  of  the  same  vessel  ? 

9.  In  swimming,  you  put  water  in  motion ;  what  causes  your  body 
to  advance?    What  propels  the  bird  in  flying? 

10.  Could  a  rocket  be  projected  in  the  usual  way  if  there  were  no 
atmosphere  ? 

11.  If  a  man  in  a  boat  moves  it  by  pulling  on  a  rope  at  one  end, 
the  other  end  being  fastened  to  a  post,  how  is  the  boat  put  in  motion  ? 
Would  it  move  either  faster  or  slower  if  the  other  end  were  fastened 
to  another  boat  free  to  move,  the  man  exerting  the  same  force  ? 

12.  An  ounce  bullet  leaves  a  gun  weighing  8  pounds  with  a  velocity 
of  800  feet  per  second.     W'hat  is  the  maximum  velocity  of  the  gun's 
recoil? 

13.  A  boat  of  mass  5  tons  moves  at  the  rate  of  4  miles  an  hour ; 
another  boat  of  3  tons  moves  at  the  rate  of  10   miles  an  hour. 
Compare  their  momenta. 

14.  Two  balls  whose  masses  are  respectively  10k  and  4k  have 
equal  momenta.     If  the  velocity  of  the  first  be  40  m  per  sec.,  what  is 
the  velocity  of  the  other  ? 


82  GENERAL  DYNAMICS. 


Section  VI. 

APPLICATIONS  OF  THE  THREE  LAWS  OF  MOTION. —  CENTER 
OF    GRAVITY. 

72.  Ceuter  of  Gravity  Defined.  —  Let  Figure  81  repre- 
sent any  body  of  matter;  for  instance,  a  stone.  Every 
molecule  of  the  body  is  acted  upon  by  the  force  of  gravity. 
The  forces  of  gravity  of-  all  the  mole- 
cules form  a  set  of  parallel  forces  act- 
ing vertically  downward,  the  resultant 
of  which  equals  their  sum,  and  has  the 
same  direction  as  its  components.  The 
resultant  passes  through  a  definite 
point  in  whatever  position  the  body 
may  be,  and  this  point  is  called  its  cen- 
ter of  gravity.  The  center  of  gravity 
(e.g.)  of  a  body  is,  therefore,  the  point  of  application  of  the 
resultant  of  all  these  forces;  and  for  practical  purposes  the 
whole  weight  of  the  body  may  be  supposed  to  be  concentrated 
at  its  center  of  gravity. 

Let  G  in  the  figure  represent  this  point.  For  practical 
purposes,  then,  we  may  consider  that  gravity  acts  only 
upon  this  point,  and  in  the  direction  GF.  If  the  stone 
falls  freely,  this  point  cannot,  in  obedience  to  the  first  law 
of  motion,  deviate  from  a  vertical  path,  however  much  the 
body  may  rotate  about  this  point  during  its  fall.  Inas- 
much, then,  as  the  e.g.  of  a  falling  body  always  describes 
a  definite  path,  a  line  GF  that  represents  this  path,  or  the 
path  in  which  a  body  supported  tends  to  move,  is  called 
the  line  of  direction. 

It  is  evident  that  if  a  force  is  applied  to  a  body  equal  to 


APPLICATIONS   OF  THE  THREE  LAWS   OF  MOTION.      83 

its  own  weight,  and  opposite  in  direction,  and  anywhere  in 
the  line  of  direction  (or  its  continuation),  this  force  will 
be  the  equilibrant  of  the  forces  of  gravity ;  in  other  words, 
the  body  subjected  to  such  a  force  is  in  equilibrium, 
and  is  said  to  be  supported,  and  the  equilibrant  is  called 
its  supporting  force.  To  support  any  body,  then,  it  is 
only  necessary  to  provide  a  support  for  its  center  of  grav- 
ity. The  supporting  force  must  be  applied  somewhere  in 
the  line  of  direction,  otherwise  the  body  will  fall.  The  dif- 
ficulty of  poising  a  book,  or  any  other  object,  on  the 
end  of  a  finger,  consists  in  keeping  the  support  under  the 
center  of  gravity. 

Figure  82  represents  a  toy  called  a  "  witch,"  consisting  of  a  cylinder  of 
pith  terminating  in   a  hemisphere  of  lead. 
The  toy  will  not  lie  in  a  horizontal  position, 
as  shown  in  the  figure,  because  the  support 
is  not  applied  immediately  under  its  e.g.  at 
G;  but  when  placed  horizontally,  it  immedi- 
ately assumes  a  vertical  position.    It  appears  Flg*  82* 
to  the  observer  to  rise;   but,  regarded  in  a   mechanical  sense,  it  really 
falls,  because  its  e.g.,  where  all  the  weight  is  supposed  to  be  concentrated, 
takes  a  lower  position. 

73.    How  to  Find  the  Center  of  Gravity  of  a  Body.  — 

Imagine  a  string  to  be  attached  to 
a  potato  by  means  of  a  tack,  as  in 
Figure  83,  and  to  be  suspended 
from  the  hand.  When  the  potato 
is  at  rest,  there  is  an  equilibrium 
of  forces,  and  the  e.g.  must  be  some- 
where in  the  line  of  direction  an ; 
hence,  if  a  knitting-needle  is  thrust 
vertically  through  the  potato  from 
a,  so  as  to  represent  a  continuation  Fig*  83* 

of  the  vertical  lice  oa,  the  e.g.  must  lie  somewhere  in  the 


84  GENERAL    DYNAMICS. 

path  an  made  by  the  needle.  Suspend  the  potato  from 
some  other  point,  as  5,  and  a  needle  thrust  vertically 
through  the  potato  from  b  will  also  pass  through  the  e.g. 
Since  the  e.g.  lies  in  both  the  lines  an  and  6s,  it  must  be  at 
£,  their  point  of  intersection.  It  will  be  found  that,  from 
whatever  point  the  potato  is  supported,  the  point  c  will 
always  be  vertically  under  the  point  of  support.  On  the 
same  principle  the  e.g.  of  any  body  is  found.  But  the 
e.g.  of  a  body  may  not  be  coincident  with  any  particle  of 
the  body ;  for  example,  the  e.g.  of  a  ring,  a  hollow 
sphere,  etc. 

74.  Equilibrium  of  Bodies.  —  A  body  will  rest  in 
equilibrium  when  its  line  of  direction  passes  through  its 
point  of  support.  A  body  will  be  supported  at  its  base 
when  its  line  of  direction  falls  within  its  base  or  lowest 
side.  [The  base  of  any  body,  e.g.  a  chair,  is  the  polygon 
formed  by  joining  by  straight  lines  the  points  of  support.] 
There  are  three  kinds  of  equilibrium  :  — 

(1)  A  body  so  supported  that  when  slightly  disturbed  it  tends  to  return 
to  its  original  position,  is  said  to  be  in  stable  equilibrium.     This  will  be 
the  case  whenever  such  a  disturbance  raises  its  e.g.,  for  the  weight  of  the 
body  acting  at  its  e.g.  tends  to  bring  this  point  as  low  as  possible  and 
thus  causes  it  to  return  to  its  former  position.     A  supported  body  is  in 
stable  equilibrium  if  its  e.g.  be  as  low  as  possible.     Evidently  a  body  is 
in  stable  equilibrium  when  the  supporting  force  is  applied  in  the  line  of 
direction  above  its  e.g. 

(2)  A  body  so  supported  that  a  slight  disturbance  tends  to  cause  it  to 
take  a  new  position  with  its  e.g.  lower  than  before  is  in  unstable  equi- 
librium. 

(3)  A  supported  body  whose  e.g.  is  neither  raised  nor  lowered  by  a 
disturbance  (e.g.  a  sphere  on  a  horizontal  plane)  is  in  neutral  equilibrium. 

Experiment  66.  —  Try  to  support  a  ring  on  the  end  of  a  stick,  as 
at  b  (Fig.  84).  If  you  can  keep  the  support  exactly  under  the  e.g.  of 


APPLICATIONS   OF   THE   THREE   LAWS   OF   MOTION.       85 


the  ring,  there  will  be  an  equilibrium  of  forces,  and  the  ring  will  re- 
main at  rest.  But  if  it  is  slightly  disturbed,  the-  equilibrium  will  be 
destroyed,  and  the  ring  will  fall.  Support  it  at  a ;  in  this  position  its 
e.g.  is  as  low  as  possible,  and  any  disturbance  will  raise  its  e.g. ;  but, 
in  consequence  of  the  tendency  of  the  e.g.  to  get  as  low  as  possible,  it 
will  quickly  fall  back  into  its  original  position. 


Fig.  84.  Fig.  85. 

Experiment  67.  —  Prepare  a  V-shaped  frame  like  that  shown  in 
Figure  85,  the  bar  AC  being  about  three  feet  long ;  place  it  so  that 
the  end  will  overlap  the  table  two  or  three  inches,  and  hang  a  heavy 
weight  or  a  pail  of  water  on  the  hook  B,  and  the  whole  will  be  sup- 
ported. Rock  the  weight  back  and  forth  by  raising  the  end  C  and 
allowing  it  to  fall.  What  kind  of  equilibrium  is  this?  Remove  the 
weight,  and  the  bar  falls  to  the  floor.  Why  ? 

The  stability  of  a  body  varies  with  its  breadth  of  base,  and 
inversely  with  the  hight  of  its  e.g.  above  its  base.  Support 
a  book  on  a  table  so  that  it  may  have  three  different 
degrees  of  stability,  and  account  for  the  same. 

QUESTIONS. 

1.  Why  is  a  person's  position  more  stable  when  his 
feet  are  separated  a  little,  than  when  close  together  ? 

2.  How  does  ballast  tend  to  keep  a  vessel  from  over- 
turning ? 

3.  For  what  two  reasons  is  a  pyramid  a  very  stable 
structure  ? 

4.  What  point  in  a  falling  body  descends  in  a  straight       Fig.  86. 


86  GENERAL  DYNAMICS. 

line?    What  is  this  line  called?    Disregarding  the  motions  of  the 
earth,  toward  what  point  in  the  earth  does  this  line  tend  ? 

5.  It  is  difficult  to  balance  a  lead-pencil  on  the  end  of  a  finger ; 
but  by  attaching  two  knives  to  it,  as  in  Figure  86,  it  may  be  rocked 
to  and  fro  without  falling,  Explain. 


Section  VII. 

APPLICATIONS  OF  THE  THREE  LAWS  OF  MOTION  CONTIN- 
UED.—  EFFECT  OF  A  CONSTANT  FORCE  ACTING  ON  A 
BODY  PERFECTLY  FREE  TO  MOVE.  —  FALLING  BODIES. 

75.  Any  Force,  however  Small,  can  move  any  Body 
of  however  Great  Mass.  —  For  example,  a  child  can  move 
a  body  having  a  mass  equal  to  that  of  the  earth,  pro- 
vided only  that  the  motion  of  this  body  is  not  hindered 
by  a  third  body.  Moreover,  the  amount  of  momentum 
that  the  child  can  generate  in  this  immense  body  in  a 
given  time  is  precisely  the  same  as  that  which  it  would 
generate  by  the  exertion  of  the  same  force  for  the  same 
length  of  time  on  a  body  having  a  mass  of  (say)  10  pounds. 
Momentum  is  the  product  of  mass  into  velocity;  so,  of 
course,  as  the  mass  is  large,  the  velocity  acquired  in  a 
given  time  will  be  correspondingly  small.  The  instant  the 
child  begins  to  act,  the  immense  body  begins  to  move. 
Its  velocity,  infinitesimally  small  at  the  beginning,  would 
increase  at  almost  an  iniinitesimally  slow  rate,  so  that  it 
might  be  months  or  years  before  its  motion  would  become 
perceptible.  It  is  easy  to  see  how  persons  may  get  the 
impression  that  very  large  bodies  are  immovable  except 
by  very  great  forces.  The  erroneous  idea  is  acquired  that 


APPLICATIONS   OF   THE  THREE  LAWS   OF   MOTION.       87 

bodies  of  matter  have  a  power  to  resist  the  action  of  forces 
in  causing  motion,  and  that  the  greater  the  mass,  the 
greater  the  resistance  ("  quality  of  not  yielding  to  force," 
Webster').  The  fact  is,  that  no  body  of  whatever  mass  has 
any  power  to  resist  motion  ;  in  other  words,  "  a  body  free  to 
move  cannot  remain  at  rest  under  the  slightest  unbalanced 
force  tending  to  set  it  in  motion."  Furthermore,  a  given 
force  acting  for  the  same  length  of  time  will  generate  the 
same  amount  of  momentum  in  all  bodies  free  to  move,  irre- 
spective of  their  masses. 

76.  Falling  Bodies.  —  A  constant  force  is  one  that  acts 
continuously  and  with  uniform  intensity.  Nature  fur- 
nishes no  example  of  a  body  moved  by  a  force  so 'nearly 
constant  as  that  of  a  body  falling  through  a  moderate  dis- 
tance to  the  earth.  Inasmuch  as  the  velocity  of  falling 
bodies  is  so  great  that  there  is  not  time  for  accurate  obser- 
vation during  their  fall,  we  must,  in  investigating  the  laws 
of  falling  bodies,  resort  to  some  method  of  checking  their 
velocity,  without  otherwise  changing  the  character  of  the 
fall. 

Experiment  68.  —  Ascertain,  as  in  Experiment  60,  how  far  the 
weights,  moved  by  a  constant  force  (e.g.  2  grams),  descend  during 
one  swing  of  the  pendulum.  Inasmuch  as  all  swings  of  the  pendulum 
are  made  in  equal  intervals  of  time,  we  may  take  the  time  of  one 
swing  as  our  unit  of  time.  We  will,  for  convenience,  take  for  our 
unit  of  distance  the  distance  the  weights  fall  during  the  first  unit  of 
time,  call  this  unit  a  space,  and  represent  the  unit  graphically  by  the 
line  db  (Fig.  87). 

Next  ascertain  how  far  the  weights  fall  from  the  starting-point 
during  two  units  of  time  (i.e.  two  swings  of  the  pendulum).  The 
distance  will  be  found  to  be  four  spaces,  or  four  times  the  distance 
that  they  fell  during  the  first  unit  of  time.  This  distance  is  repre- 
sented by  the  line  ac.  But  we  have  learned  that  the  weights  descend 
only  one  space  (aft)  during  the  first  unit  of  time,  hence  they  must 


GENERAL  DYNAMICS. 


1  Uof  T— 


S  Uof  T— 


descend  three  spaces  during  the  second  unit  of  time.  The  weights, 
under  the  action  of  the  constant  force,  start  from  a  state  of  rest,  and 
move  through  one  space  in  a  unit  of  time.  This  force,  continuing  to 
act,  accomplishes  no  more  nor  less  during  any  subsequent 
unit  of  time.  But  the  weights  move  through  three  spaces 
during  the  second  unit  of  time ;  hence  two  of  the  spaces 
must  be  due  to  the  velocity  they  had  acquired  at  the  end 
of  the  first  unit.  In  other  words,  if  the  ring  H  is  placed 
at  the  point  (corresponding  to  b)  reached  by  the  weights 
at  the  end  of  the  first  unit  of  time,  then  weight  E  will  be 
caught  off  (i.e.  the  constant  force  will  be  withdrawn), 
and  the  other  weights  will,  in  conformity  with  the  first 
law  of  motion,  continue  to  move  with  uniform  -velocity 
from  this  point  (except  as  they  are  retarded  by  resist- 
ance of  the  air  and  the  friction  of  the  wheel  C),  and  will 
descend  two  spaces  during  the  second  unit  and  reach 
point  e.  (Try  it.) 

The  weights,  therefore,  have  at  the  end  of  the  first 
unit  of  time  a   velocity  (V)  of  two  spaces.     But  they 
started  from  a  state   of  rest:   hence  the  constant  force 
causes,  during  the  first  unit  of  time,  an  acceleration  of 
velocity  equal  to  two  spaces. 

Let  the  weights  descend  three  units  of  time,  and  it  will  be  found 
that  the  weights  will  descend  in  this  time  nine  spaces  (ac?),  or  five 
spaces  (cd)  during  the  third  unit  of  time.  One  of  these  five  spaces 
is  due  to  the  action  of  the  force  during  the  third  unit  of  time ;  the 
weights  must  then  have  had  at  point  c  (i.e.  at  the  end  of  the  second  unit 
of  time)  a  velocity  of  four  spaces.  But  at  the  end  of  the  first  unit 
of  time  they  had  a  velocity  of  two  spaces ;  then  they  must  have  .gained 
during  the  second  unit  of  time  a  velocity  of  two  spaces.  It  seems, 
then,  that  the  effect  of  a  constant  force  applied  to  a  body  is  to  produce 
uniformly  accelerated  motion  when  there  are  no  resistances. 

The  velocity  of  a  body  at  any  instant  is  the  distance  which  it  would 
traverse  in  a  unit  of  time  if  its  motion  should  continue  unchanged 
during  that  time.  Acceleration  is  the  change  of  velocity  in  a  unit  of 
time.  The  acceleration  due  to  gravity  is  usually  represented  by  g, 
and  is  always  twice  the  distance  (^  g)  traversed  during  the  first  unit 
of  time.  When  a  body  is  acted  upon  by  any  other  constant  force, 
the  acceleration  produced  by  the  force  is  usually  represented  by  the 
letter  A. 


s  Uof  T— 
Fig.  87. 


APPLICATIONS   OF  THE  THREE  LAWS   OF  MOTION.       89 


Arrange  the  results  of  your  observations  in  a  tabulated  form  as 
follows :  — 


No.  of  units  of 
time. 

Total  distance 
passed  over. 
(S) 

Distance  passed 
over   in    each 
unit;    also  av- 
erage velocity. 
(s) 

Velocity  at  the 
end    of    each 
unit. 
(V) 

Increase  of  ve- 
locity in  each 
unit,    i.e.    ac- 
celeration. 

1 

1(M) 

10  9) 

2  0  £) 

2  Q  </) 

2 

4      " 

3      « 

4      « 

2      « 

3 

9      " 

5      " 

6      " 

2      " 

4 

16      " 

7      « 

8      " 

2      « 

etc. 

etc. 

etc. 

etc. 

etc. 

77.    Formulas  for  Uniformly  Accelerated  Motion. — 

If  we  substitute  A  for  #,  and  represent  the  distance 
traversed  during  a  given  unit  of  time  by  s,  and  the  total 
distance  the  body  has  accomplished  from  the  outset  to 
the  end  of  a  given  unit  of  time  (T)  by  S,  we  derive  from 
our  tabulated  results  the  following  formulas  for  solving 
problems  of  uniformly  accelerated  motion:  — 

(1)  V= 

(2)  ,  = 

(3)  S  = 

Hence,  (1)  the  velocity  acquired  varies  as  the  time;  (2)  the 
spaces  passed  over  in  successive  equal  intervals  of  time  vary 
as  the  odd  numbers  1,  3,  5,  7,  etc. ;  and  (3)  the  entire  space 
traversed  varies  as  the  square  of  the  time. 

Strictly  speaking,  a  falling  body  is  not  under  the  influence  of  a  constant 
force,  inasmuch  as  gravity  varies  inversely  as  the  square  of  the  distance 
from  the  center  of  the  earth.  But  for  small  distances  the  variation  may 
be,  for  all  practical  purposes,  disregarded,  as  at  a  hight  of  a  kilometer 
(about  f  of  a  mile)  it  is  only  about  yfa-g  of  the  weight  at  the  surface.  It 
can  be  shown  mathematically  that  the  velocity  that  would  be  acquired  by 
a  body  falling  freely  to  the  earth's  surface  from  an  infinite  distance  would 
be  about  35  000  feet  per  second. 


90  GENERAL  DYNAMICS. 

78.  Velocity  of  a  Falling  Body  Independent  of  its 
Mass  and  Kind  of  Matter.  —  If  we  grasp  a  coin  and  a  bit 
of  paper  between  the  thumb  and  finger,  and  release  both 
at  the  same  instant,  the  coin  will  reach  the  floor  first.  It 
would  seem  as  though  a  heavy  body  falls  faster  than  a 
light  body.  Galileo  was  the  first  to  show  the  falsity  of 
this  assumption.  He  let  drop  from  an  eminence  iron  balls 
of  different  weights :  they  all  reached  the  ground  at  the 
same  instant.  Hence  he  concluded  that  the  velocity  of  a 
falling  body  is  independent  of  its  mass. 

He  also  dropped  balls  of  wax  with  the  iron  balls.     The 
iron  balls  reached  the  ground  first.     Are  some  kinds  of 
matter  affected  more  strongly  by  gravitation  than 
others?    If  a  coin  and  several   bits  of  paper   are 
placed  in  a  long  glass   tube   (Fig.  88),  the  air  ex- 
hausted, and  the  tube  turned  end  for  end,  it  will 
be  found  that  the  coin  and  the  paper  will  fall  with 
equal  velocities.    Hence,  the  earth  attracts  all  matter 
alike.     A  wax  ball  of  the  same  size  as  an  iron  ball 
meets  with  the  same  resistance  from  the  air  that 
the  iron  ball  does ;  but  since  the  mass  of  the  former 
is  less  than  that  of  the  latter,  the  force  acting  on 
the  former  is  less,  and  a   less  force  cannot  over- 
come  the  same  resistance  as  quickly,  consequently 
88*     in  the  air  the  wax  ball  falls  a  little  more  slowly. 
We  conclude,  therefore,  that  in  a  vacuum  all  bodies  fall 
with  equal  velocities. 

Experiments  show  that  in  the  latitude  of  the  Northern 
States  the  acceleration,  i.e.  the  value  of  #,  is,  near  sea-level 
and  in  a  vacuum,  32|-  feet  (9.8m)  per  second;  that  is,  the 
velocity  gained  by  a  falling  body,  disregarding  the  resist- 
ance of  the  air,  is  32J  feet  per  second,  and  the  body  falls 
in  the  first  second  16^  feet  (4.9m). 


APPLICATIONS   OF  THE  THREE  LAWS   OF  MOTION.       91 


M 


Fig.  89. 

What  is  its  average  velocity 


EXERCISES. 

1.  What  is  a  constant  force?   What  effect  does  it  produce  on  every 
body  wnen  there  are  no  resistances? 

2.  (a)  How  far  will     A  B  C  D 

a  body  fall  in  a  vacuum   E£^         ---JK 

in  one  second?  (6)  What 
is  its  velocity  at  the  end   F 
of  the  first  second?   (c) 
What  is  its  acceleration 
per  second? 

3.  (a)  How  far  will  a  G 
body  fall  in  ten  seconds? 

(b)  How  far  will  it  fall 

in    the   tenth  second?     p 

(c)  What  is  its  velocity 

at  the  end  of  the  tenth  second? 
during  the  tenth  second  ? 

4.  (a)  How  far  will  a  body  fall  in  one-fourth  of  a  second  ? 
is  the  velocity  of  a  falling  body  at  the 

end  of  the  first  quarter  of  a  second  of 
its  fall? 

5.  A  body  is  projected  from  point 
A  (Fig.  89)  in  the  horizontal  direction 
AH.     (a)  If  there  were  no  resistance 
of  the  air,  and  gravity  did  not  act  on 
it,  it  would  go  a  distance  during  the 
first  unit  of  time  represented  by  AB ; 
how  far  would  it  go  during  the  second 
and  third  units   of  time?    (In  every 
answer    quote   the    law  of  motion  in 
conformity  with  which  your  answer  is 
given.)     (6)  If  the  body  were  dropped 
from  A,  it  would  reach  successively 
points  E,  F,  and  G  at  the  ends  of  the 
first,  second,  and  third  units  of  time. 
If  the  body  were  projected  horizontally 
in  the  direction  AH,  and  gravity  acts 

during  its  flight,  what  points  will  the  Fig.  90. 

body  successively  reach  at  the  end  of  the  same  units  of  time  ? 


92  GENERAL  DYNAMICS. 

6.  (a)  Suppose  that  a  body  is  projected  obliquely  upward  m  the 
direction  AH  (Fig.  90),  (gravity  meantime  acting  on  the  body) ;  what 
points  will  the  body  reach  successively  at  the  end  of  the  first,,  second, 
and  third  units  of  time?     (6)  How  far  will  the  ascending  body  vir- 
tually fall  during  the  first  unit  of  time?     (c)  How  far  during  the 
second  unit?   (d)  How  far  during  the  third  unit?    (e)  Show  that  your 
answers  are  consistent  with  the  Second  Law  of  Motion. 

7.  (a)  Under  the  action  of  a  constant  force,  a  body  meeting  with  no 
resistances  moves  from  a  state  of  rest  20  feet  during  the  first  minute : 
how  far  will  it  go  in  an  hour?    (&)  Suppose  at  the  end  of  the  first 
minute  the  force  should  cease  to  act,  how  far  would  the  body  go  in  an 
hour  from  that  instant  ? 


Section  VIII. 

APPLICATIONS   OF   THE  THREE  LAWS   OF   MOTION   CONTIN- 
UED. —  CURVILINEAR    MOTION. 

79.  How  Curvilinear  Motion  is  Produced.  —  Motion 
is  curvilinear  when  its  direction  changes  at  every  point. 
But  according  to  the  first  law  of  motion,  every  moving 
body  proceeds   in   a   straight   line,    unless    compelled   to 
depart  from  it  by  some  external  force.     Hence  curvilinear 
motion  can  be  produced  only  by  an  external  force  acting 
continuously  upon  the  body  at  an  angle  to  the  straight 
path  in  which  the  body  tends  to  move,  so  as  constantly 
to  change  its   direction.      In  case   the   body  moves  in  a 
circle,  this  force  acts  at  right  angles  to  the  path  of  the 
body  or  towards  the  center  of  motion  ;  hence  this  deflecting 
force  has  received  the  name  of  centripetal  force. 

80.  Centrifugal  Tendency. 

Experiment  69.  —  Cause  a  ball  to  revolve  around  your  hand  by 
means  of  a  string  attached  to  it  and  held  in  the  hand.     Observe 


APPLICATIONS    OF    THE    THREE    LAWS    OF    MOTION.      93 

closely  every  phase  of  the  operation.  First,  you  make  a  movement  as 
if  to  project  the  ball  in  a  straight  line.  Immediately  you  begin  to 
pull  on  the  string  to  prevent  its  going  in  a  straight  line.  By  a  con- 
tinuous exertion  of  these  two  forces  in  a  short  time  the  ball  acquires 
great  speed.  You  may  now  cease  to  exert  any  projecting  force,  and 
simply  keep  the  hand  still ;  but  as  the  ball  has  acquired  a  motion, 
and  all  motion  tends  to  be  in  a  straight  line,  you  are  still  obliged  to 
exert  a  pulling  force  to  deflect  it  from  this  path.  Observe  that  as  the 
velocity  of  the  ball  is  retarded  by  the  resistance  of  the  air,  the  pulling 
or  deflecting  force  which  you  are  obliged  to  employ  rapidly  diminishes. 
To  satisfy  yourself  that  the  ball  tends  to  move  in  a  straight  line, 
let  go  the  string  or  cut  it,  and  the  ball  immediately  moves  off  in  a 
straight  line,  or  simply  perseveres  in  the  direction  it  had  at  the 
instant  the  string  was  cut. 

The  direction  which  a  revolving  body  tends  to  move  at 
every  point  is  a  tangent  to  that  point  of  its  curvilinear 
path.  The  tendency  of  a  revolving  body  to  "  fly  off  "  tan- 
gentially  is  called  the  centrifugal  tendency.  Illustrations 
of  this  tendency  may  be  found  in  a  vehicle  turning  a 
corner,  a  stone  leaving  a  sling,  water  escaping  from  a 
rotating  grindstone,  pieces  broken  from  fly-wheels,  etc. 

In  order  that  a  body  may  move  in  a  circular  path  the 
centripetal  force  must  have  a  definite  magnitude  which 
depends  upon  the  mass  of  the  body  and  its  velocity.  Careful 
observations  have  determined  that  for  bodies  revolving  in 
circular  orbits  the  centripetal  force  (and  centrifugal  tendency) 
varies  as  the  mass  of  the  body  and  the  square  of  its  velocity. 

The  farther  a  point  is  from  the  axis  of  motion  of  a  rotating  body,  the 
farther  it  has  to  move  during  a  rotation  ;  consequently  the  greater  its 
velocity.  Hence,  bodies  situated  at  the  earth's  equator  have  the  greatest 
velocity,  due  to  the  earth's  rotation,  and  consequently  the  greatest  tendency 
to  fly  off  from  the  surface,  the  effect  of  which  is  to  neutralize,  in  some 
measure,  the  force  of  gravity.  It  is  calculated  that  a  body  weighs  about  ^\^ 
less  at  the  equator  than  at  either  pole,  in  consequence  of  the  greater  cen- 
trifugal tendency  at  the  former  place.  But  289  is  the  square  of  17 ;  hence, 


94 


GENERAL   DYNAMICS. 


if  the  earth's  velocity  were  increased  seventeen-fold,  objects  at  the  equator 

would  weigh  nothing. 

We  have  also  learned  (page  17)  that  a  body  weighs  more  at  the  poles, 

in  consequence  of  the  oblateness  of  the  earth.     This  is  estimated  to  make 

a  difference  of  about  ^-g.     Hence  a  body  will  weigh  at  the  equator  -^g-4- 

•j|^  =  (about)  T^  less  than  at  the  poles. 

The  attraction  between  the  sun  and  the  earth  causes  these  bodies  to 

move  in   curvilinear    paths, 

«    ^-  ^s.  i         performing    what   is    called 

annual  revolutions.  The 
motion  of  both  these  bodies, 
were  it  not  for  this  mutual 
attraction  (and  the  attraction 
of  other  celestial  bodies), 


Fig.  91. 


would  be  eternally  in  straight  lines,  but  in  consequence  of  their  mutual 
attraction  both  revolve  about  a  point  C  (Fig.  91),  which  is  the  center  of 
gravity  of  the  two  bodies  considered  as  one  body  (as  if  connected  by  a 
rigid  rod).  If  both  bodies  had  equal  masses,  the  center  of  gravity  and 
center  of  motion  would  be  half-way  between  the  two  bodies ;  but  as  the 
mass  of  the  earth  is  less  than  that  of  the  sun,  so  its  velocity  and  distance 
traversed  are  proportionally  greater. 


Fig.  92.  Fig.  93. 

Experiment  70.  —  Arrange  some  kind  of  rotating  apparatus,  e.g. 
R  (Fig.  92).  Suspend  a  skein  of  thread  a  (Fig.  93)  by  a  string,  and 
rotate;  it  assumes  the  shape  of  the  oblate  spheroid  a'.  Suspend  a 
glass  globe  G  (Fig.  92)  about  one-tenth  full  of  colored  water,  and 
rotate.  The  liquid  gradually  leaves  the  bottom,  rises,  and  forms  an 
equatorial  ring  within  the  glass.  This  illustrates  the  probable  method 
by  which  the  earth,  on  the  supposition  that  it  was  once  in  a  fluid 


APPLICATIONS   OF  THE  THREE  LAWS   OF   MOTION.       95 

state,  assumed  its  present  spheroidal  state.  (Explain.)  Pass  a  string 
through  the  longest  diameter  of  an  onion  c,  and  rotate;  the  onion 
gradually  changes  its  position  so  as  to  rotate  on  its  shortest  axis. 

It  may  be  demonstrated  mathematically,  as  well  as  experi- 
mentally, that  a  freely  rotating  body  is  in  stable  equilib- 
rium only  when  rotating  about  its  shortest  diameter ;  hence 
the  tendency  of  a  rotating  body  to  take  this  position. 

QUESTIONS. 

1.  (a)  What  is  the  cause  of  the  stretching  force  exerted  on  the 
rubber   cord    when    you    swing    a    return-ball    about    your   hand? 
(6)  Suppose  that  you  double  the  velocity  of  the  ball ;  how  many  times 
will  you  increase  this  stretching  force  ? 

2.  Why  do  wheels  and  grindstones,  when  rapidly  rotating,  tend  to 
break,  and  the  pieces  fly  off? 

3.  On  what  does  the  magnitude  of  the  pull  between  a  rotating  body 
and  its  center  of  motion  depend  ? 

4.  (a)  Explain  the  danger  of  a  carriage  being  overturned  in  turning 
a  corner,     (b)  How  many  fold  is  the  tendency  to  overturn  increased 
by  doubling  the  velocity  of  the  carriage? 


Section  IX. 

APPLICATION   OF  THE  THREE   LAWS   OF  MOTION  CONTIN- 
UED. —  THE  PENDULUM. 

81.    Laws  of  the  Pendulum. 

Experiment  71.  —  Suspend  iron  balls  by  strings,  as  in  Figure  94. 
Make  A  and  B  the  same  length.  Draw  A  and  B  one  side,  and  to  dif- 
ferent hights,  so  that  one  may  swing  through  a  longer  arc  than  the 
other,  and  let  both  drop  at  the  same  instant.  One  moves  much 
faster  than  the  other,  and  completes  a  longer  journey  at  each  swing, 
but  both  complete  their  swing  or  vibration  at  the  same  time. 

Hence  (1)  the  time  of  vibration  of  a  pendulum  is  (strictly  speaking, 
approximately)  independent  of  the  length  of  the  arc. 


96 


GENERAL   DYNAMICS. 


Experiment  72.  —  Set  all  the  balls  swinging ;  only  A  and  B  swing 
together,  i.e.  in  the  same  time.  The  shorter  the  pendulum,  the  faster 
it  swings.  Make  B  about  39  inches  long  from  the  point  of  sus- 
pension to  the  center  of  the  ball,  regulating 
this  length,  as  necessity  may  require,  so  that 
the  number  of  vibrations  made  by  the  pen- 
dulum in  one  minute  shall  be  exactly  60 ;  in 
other  words,  so  that  it  shall  "beat  seconds." 
(Accurately,  a  pendulum  that  beats  seconds 
is  39.09  inches  long.)  Make  C  one-fourth 
as  long  as  B.  Count  the  vibrations  made 
by  C  in  one  minute ;  it  makes  120  vibrations 
in  the  same  time  that  B  makes  60  vibrations. 
Make  D  one-ninth  the  length  of  B;  the 
former  makes  three  vibrations  while  the 
latter  makes  one.  Consequently  the  time  of 
vibration  of  the  former  is  one-third  that  of 
the  latter. 

Hence  (2)  the  time  of  vibration  of  a  pendu- 
lum varies  as  the  square  root  of  its  length. 

By  experiments  too  difficult  for  ordinary 
school  work,  it  has  been  ascertained  that 
(3)  the  time  of  vibration  of  a  pendulum  varies 
inversely  as  the  square  root  of  the  force  of 
gravity  (upon  which  the  value  of  g  depends). 
Hence  it  is  apparent  that  by  determining 
the  time  of  vibration  of  a  pendulum  of  the 
same  length,  at  different  distances  from  the 
center  of  gravity  of  the  earth  (e.g.  at  the  top  and  bottom  of  a 
mountain,  or  at  sea-level  at  different  latitudes),  the  relative  value 
of  g  at  these  places  may  be  ascertained. 

Experiment  73.  —  Loosen  the  binding-screw  in  the  bob  of  the  pen- 
dulum of  the  Atwood  machine  (Fig.  66),  and  place  the  bob  at  differ- 
ent elevations  on  the  pendulum-rod.  Count  the  number  of  vibrations 
made  by  the  pendulum  in  a  minute,  when  the  bob  is  placed  at  these 
different  elevations.  The  greater  the  elevation  of  the  bob,  —  in  other 
words,  the  shorter  the  pendulum,  — the  greater  the  number  of  vibra- 
tions made.  We  learn  by  this  experiment  that  the  time  of  vibration 
of  a  pendulum  may  be  regulated  by  raising  or  lowering  its  bob.  For 
further  development  of  the  pendulum  see  Appendix,  Section  D. 


Fig.  94. 


APPLICATIONS   OF   THE   THREE  LAWS   OF  MOTION.       97 

EXERCISES. 

1.  One  pendulum  is  20  inches  long,  and  vibrates  four  times  as  fast 
as  another.     How  long  is  the  other  ? 

2.  (a)  What  effect  on  the  rate  of  vibration  has  the  weight  of  its 
bob?    (5)  What  effect  has  the  length  of  the  arc?     (c)  What  affects 
the  rate  of  vibration  of  a  pendulum  ? 

3.  How  can  you  quicken  the  vibration  of  a  pendulum  threefold? 

4.  A  clock  loses  time,  (a)    What  change  in  the  pendulum  ought  to 
be  made?     (6)  How  would  you  make  the  correction? 

5.  Two  pendulums  are  four  and  nine  feet  long  respectively.    While 
the  short   one  makes  one  vibration,  how  many  will  the  long   one 
make  ? 

6.  How  long  is  a  pendulum  that  makes  two  vibrations  in  a  second  ? 

7.  What  is  the  time  of  vibration  of  a  pendulum  (39.09  -r-  4  =)  9.75  in. 
long? 

8.  The  number  of  vibrations  made  by  a  given  pendulum  in  a  given 
time  varies  as  the  square  root  of  the  force  of  gravity.     Force  of  grav- 
ity at  any  place  is  expressed  by  the  value  of  g  (i.e.  by  the  acceleration 
which  it  produces),     (a)  If  at  a  certain  place  a  pendulum  39.09  in. 
long  make  3600  vibrations  in  an  hour,  and  the  value  of  g  is  32.16  ft., 
what  is  the  acceleration  at  a  place  where  the  same  pendulum  makes 
3590  vibrations  in  the  same  time?     (6)  Which  of  the  two  places  is 
nearer  the  center  of  gravity  of  the  earth  ? 

9.  Suggest  some  way  by  which  the  force  of  gravity  at  different 
latitudes  and  altitudes  may  be  determined. 

10.  (a)  A  certain  body  weighs  12  Ibs.  where  the  value  of  g  is  32.16  ft. ; 
what  will  the  same  body  weigh  at  a  place  wher,e  g  —  32  ft.  ?     (b)  Sup- 
pose that  the  former  place  is  at  the  surface  of  the  earth  and  4000  miles 
from  the  earth's  center  of  gravity;  how  far  above  it  is  the  latter  place? 
(See  page  16.) 

11.  A  pebble  is  suspended  by  a  thread  2  ft.  long;   required  the 
number  of  vibrations  it  will  make  in  a  minute. 

12.  Why  do  not  heavy  bodies  fall  faster  than  light  ones  in  a  vacuum? 

13.  Take  equal  masses  of  wood  and  lead ;  which  weighs  more  ? 

14.  A  stone  falls  from  the  top  of  a  railway  carriage  which  is  mov- 
ing at  the  rate  of  one-half  of  a  mile  a  minute.     Find  what  horizontal 
distance  and  what  vertical  distance  the  stone  will  have  passed  through 
in  one-tenth  of  a  second,  disregarding  the  resistance  of  the  air. 

Ans.  4.4ft.;  .16ft. 


CHAPTER   IV. 
WORK  AND  ENERGY. 

Section  I. 

METHODS  OF  ESTIMATING  WORK  AND  ENERGY. 

82.  Work. —  Whenever  a  force  causes  motion,  it  does 
work.  A  force  may  act  for  an  indefinite  time  without 
doing  work ;  for  example,  a  person  may  support  a  stone 
for  a  time  and  become  weary  from  the  continuous  appli- 
cation of  force  to  prevent  its  falling,  but  he  does  no  work 
apon  the  stone  because  he  effects  no  change.  When  a 
force  acts  through  space,  work  is  done.  Let  the  person 
holding  the  weight  exert  just  a  little  more  force ;  the 
weight  will  rise,  and  work  will  be  done. 

A  body  that  is  moved  is  said  to  have  work  done  upon  it  ; 
and  a  body  that  moves  another  body  is  said  to  do  work 
upon  the  latter.  When  the  heavy  weight  of  a  pile-driver 
is  raised,  work  is  done  upon  it;  when  it  descends  and 
drives  the  pile  into  the  earth,  work  is  done  upon  the  pile, 
and  the  pile  in  turn  does  work  upon  the  matter  in  its 
path. 

The  act  of  doing  work  may  consist  in  a  mere  transfer  of 
energy  from  the  body  doing  work  to  the  body  on  which  work 
is  done,  or  it  may  consist  in  a  transformation  of  energy  from 
one  kind  to  some  other  kind,  as  when  the  pile-driver  strikes 


METHODS   OF   ESTIMATING   WORK   AND   ENERGY.        99 

the  pile  and  the  pile  is  forced  into  the  earth,  a  part  of  the 
energy  concerned  in  each  case  is  transformed  into  heat, 
which  we  shall  learn  farther  on  is  molecular  energy. 

In  future  chapters  we  shall  discuss  the  subject  of  transformations  of 
energy ;  for  the  present  our  discussions  relate  chiefly  to  transferences  of 
energy. 

83.  Formulas  for  Estimating  Work.  —  Force  and  space 
(or  distance)  are  the  essential  elements  of  work,  and  neces- 
sarily are  the  quantities  employed  in  estimating  work.  A 
given  force  acting  through  a  space  of  one  foot,  in  raising 
a  weight,  does  a  certain  amount  of  work;  it  is  evident 
that  the  same  force  acting  through  a  space  of  two  feet 
would  do  twice  as  much  work.  Hence  the  general  formula 

FS  =  W,  (1) 

in  which  F  represents  the  force  employed,  S  the  space 
through  which  the  force  acts,  and  W  the  work  done. 

In  case  a  force  encounters  resistance,  the  magnitude  of 
the  force  necessary  to  produce  motion  varies  as  the  resist- 
ance. Often  the  work  done  upon  a  body  is  more  con- 
veniently determined  by  multiplying  the  resistance  by  the 
space  through  which  it  is  overcome,  and  our  formula  becomes 
by  substitution  of  R  (resistance)  for  F  (the  force  which 
overcomes  it) 

RS  =  W.  (2) 

For  example,  a  ball  is  shot  vertically  upward  from  a  rifle 
in  a  vacuum ;  the  work  done  upon  the  ball  (by  the  explo- 
sive force  of  the  gunpowder)  may  be  estimated  by  multi- 
plying the  average  force  (difficult  to  ascertain)  exerted 
upon  it,  by  the  space  through  which  the  force  acts  (a  little 
greater  than  the  length  of  the  barrel) ;  or  by  multiplying 
the  resistance  to  motion  offered  by  gravity,  i.e.  its  weight 
(easily  ascertained)  by  the  distance  the  ball  ascends. 


100  WORK   AND   ENERGY. 

84.  Energy,  Kinetic  and  Potential.  —  Every  moving 
body  can  impart  motion ;  hence  it  can  do  work  upon  an- 
other body,  and  is  therefore  said  to  possess  energy.  The 
energy  of  a  body  is  its  "  capacity  to  do  work."  The  energy 
which  a  body  possesses  in  consequence  of  its  motion  is 
called  kinetic  energy. 

A  stone  lying  on  the  ground  is  devoid  of  energy.  Raise 
it  and  place  it  on  a  shelf;  in  so  doing  you  perform  work 
upon  it.  As  you  look  at  it  lying  motionless  upon  the  shelf, 
it  appears  as  devoid  of  energy  as  when  lying  on  the  earth. 
Attach  one  end  of  a  cord  to  it  and  pass  it  over  a  pulley 
and  wind  a  portion  of  the  cord  around  the  shaft  connected 
with  a  sewing-machine,  coffee-mill,  lathe,  or  other  con- 
venient machine.  Suddenly  withdraw  the  shelf  from  be- 
neath the  stone.  The  stone  moves;  it  communicates  motion 
to  the  machinery,  and  you  may  sew,  grind  coffee,  turn 
wood,  etc.,  with  the  energy  given  to  the  machine  by  the 
stone. 

The  work  done  on  the  stone  in  raising  it  was  not  lost ; 
the  stone  pays  it  back  while  descending.  There  is  a  very 
important  difference  between  the  stone  lying  on  the  floor, 
and  the  stone  lying  on  the  shelf:  the  former  is  powerless 
to  do  work;  the  latter  can  do  work.  Both  are  alike 
motionless,  and  you  can  see  no  difference,  except  an 
advantage  that  the  latter  has  over  the  former  in  having 
a  position  such  that  it  can  move.  What  gave  it  this 
advantage?  Work.  A  body,  then,  may  possess  energy 
due  merely  to  ADVANTAGE  OF  POSITION,  derived  always 
from  work  bestowed  upon  it.  Energy  due  to  advantage  of 
position  is  called  potential  energy.  We  see,  then,  that 
energy  may  exist  in  either  of  two  widely  different  states. 
It  may  exist  as  actual  motion,  or  it  may  exist  in  a  stored-up 
condition,  as  in  the  stone  lying  on  the  shelf. 


METHODS   OF   ESTIMATING   WORK  AND  ENERGY.     101 

Possibly  some  will  object  that  the  work  done  is  performed  by  gravity, 
and  not  by  the  stone  ;  that  if  this  force  should  cease  to  exist,  the  stone 
would  not  move  when  the  shelf  is  removed,  and  consequently  no  work 
would  be  done.  All  this  is  very  true,  and  it  is  likewise  true  that  when 
the  stone  is  on  the  ground,  the  same  force  of  gravity  is  acting,  but  can  do 
no  work  simply  because  the  position  of  things  is  such  that  the  stone  cannot 
move.  The  energy  which  the  stone  on  the  shelf  possesses  is  due  to  the  fact 
that  its  position  is  such  that  it  can  move,  and  that  there  is  a  stress  between 
it  and  the  earth  which  will  cause  it  to  move.  Both  advantage  of  position 
and  stress  are  necessary,  but  the  former  is  attained  only  by  work  per- 
formed. The  force  of  gravity  is  employed  to  do  work,  as  when  mills  are 
driven  by  falling  water  ;  but  the  water  must  first  be  raised  from  the  ocean- 
bed  to  the  hillside  by  the  work  of  the  sun's  heat.  The  elastic  force  of 
springs  is  employed  as  a  motive  power;  but  this  power  is  due  to  an  advan- 
tage of  position  which  the  molecules  of  the  springs  have  first  acquired  by 
work  done  upon  them. 

We  are  as  much  accustomed  to  store  up  energy  for  future  use  as  pro- 
visions for  the  winter's  consumption.  We  store  it  when  we  wind  up  the 
spring  or  weight  of  a  clock,  to  be  doled  out  gradually  in  the  movements 
of  the  machinery.  We  store  it  when  we  bend  the  bow,  raise  the  hammer, 
condense  air,  and  raise  any  body  above  the  earth's  s.urfpjce.  ;  '•;»,' 


A  body  possesses  potential  energy  ivKen^  in  mrfye\b*  \work 
done  upon  it,  it  occupies  a  position  of  advantage,  or  its  mole- 
cules occupy  positions  of  advantage,  so  that  the  energy  ex- 
pended can  be  at  any  time  recovered  by  the  return  of  the  body 
to  its  original  position,  or  by  the  return  .of  its  molecules  to 
their  original  positions. 

85.  Unit  of  Work  and  Energy.  —  Inasmuch  as  a 
body's  capacity  to  do  work  is  dependent  wholly  upon 
the  work  which  has  been  done  upon  it,  it  is  evident  that 
both  work  and  energy  may  be  measured  by  the  same  unit. 
The  unit  adopted  is  the  work  done  or  energy  imparted  in 
raising  one  pound  through  a  vertical  hight  of  one  foot.  It 
is  called  a  foot-pound.  (The  metric  unit  is  the  work  done 
or  energy  imparted  in  raising  lk  to  a  vertical  hight  of 


102  WORK   AND  ENERGY. 

lra,  and  is  called  a  kilogram  meter.)  Since  the  work  done 
in  raising  1  pound  1  foot  high  is  1  foot-pound,  the  work  of 
raising  it  10  feet  high  is  10  foot-pounds,  which  is  the  same 
as  the  work  done  in  raising  10  pounds  1  foot  high ;  and 
the  same,  again,  as  raising  2  pounds  5  feet  high. 

In  this  unit,  and  by  means  of  formulas  (1)  and  (2),  page 
99,  we  are  able  to  estimate  any  species  of  work,  and  thereby 
compare  work  of  any  kind  with  that  of  any  other  kind. 
For  instance,  let  us  compare  the  work  done  by  a  man  in 
sawing  through  a  stick  of  wood,  whose  saw  must  move  100 
feet  (S)  against  an  average  resistance  (R)  of  20  pounds, 
with  that  done  by  a  bullet  in  penetrating  a  plank  to  the 
depth  of  2  inches  Q-  foot)  against  an  average  resistance  of 
500  pounds.  Moving  a  saw  100  feet  against  a  resistance 
of  20  pounds  is  equivalent  to  raising  20  pounds  100  feet 
high,  or  doing  (RS  =  20  X  100  =)  2,000  foot-pounds  of  work 
(W)  ;*a  bullet  -moving^-  -foot  against  500  pounds'  resistance 
does  the  same  amount  of  work  as  is  required  to  raise  500 
po-iinds^-  foot  faigh,  or-  (500  X  £=)  83.3  +  foot-pounds  of 
work.  Hence  (2,000  •*  83.3  — )  about  24  times  as  much 
work  is  done  by  the  sawyer  as  by  the  bullet. 

Let  us  estimate  the  energy  stored  in  a  bow,  by  an  archer  whose  hand 
in  pulling  on  the  string,  while  bending  the  bow  moves  6  inches  Q  foot) 
against  an  average  resistance  of  20  pounds.  Here  RS  =  20  X  f  =  10 
foot-pounds  of  work  done  upon  the  bow,  or  10  foot-pounds  of  energy 
stored  in  the  bow. 

86.     Distinction    between    Energy    and     Force.  — 

W  (i.e.  energy  transmitted)  =  FS  (p.  99)  ;  hence  force  is 
only  a  factor  of  energy.  A  body  must  be  set  in  motion  or 
have  some  form  of  energy  conferred  upon  it  before  it  can 
exert  force,  so  that  force  is  merely  a  manifestation  of 
energy.  Force  can  be  increased  indefinitely  by  means  of 
machines,  as  a  lever,  hydrostatic  press,  etc. ;  energy  cannot 
be  increased  by  any  instrument  or  means  whatsoever. 


METHODS   OF   ESTIMATING   WORK   AND   ENEEGY.      103 

87.    Formula  for  Calculating  Kinetic  Energy.  —  The 

kinetic  energy  of  a  moving  body  is  calculated  by  means  of 
the  following  formula  :  — 

WV2 

—  =  energy, 

in  which  W  represents  the  weight  of  the  body,  V  its  ve- 
locity, and  g  the  acceleration  (in  this  latitude  32^  feet,  or 
9.8m  per  second)  due  to  gravity.  [For  the  derivation  of  this 
formula,  see  the  Author's  Principles  of  Physics,  pages  91 
and  92.]  For  example,  the  energy  of  a  cannon-ball  weighing 
50  pounds  and  moving  with  a  velocity  of  1,000  feet  per  sec- 


ond =        -  =    p  X  -  (about)  779,301  foot-pounds. 

2  X 


Certain  deductions  from  this  formula  should  be  strongly 
impressed  upon  the  mind  ;  viz.,  (1)  with  the  same  velocity 
the  kinetic  energy  of  a  body  varies  as  its  weight  ;  (2)  with 
the  same  weight  its  kinetic  energy  varies  as  the  square  of  its 
velocity.  Doubling  the  velocity  multiplies  the  energy  four- 
fold ;  trebling  the  velocity  multiplies  it  ninefold.  A  bullet 
moving  with  a  velocity  of  600  feet  per  second  will  pene- 
trate, not  twice,  but  four  times,  as  far  into  a  plank  as  one 
having  a  velocity  of  300  feet  per  second. 

A  railway  train  having  a  velocity  of  20  miles  an  hour 
will,  if  the  steam  is  shut  off,  continue  to  run  four  times  as 
far  as  it  would  if  its  velocity  were  10  miles  an  hour.  The 
reason  is  apparent  why  light  substances,  even  so  light  as 
air,  exhibit  great  energy  when  their  velocity  is  great. 

88.  Wasted  Work.  —  As  a  stone  is  raised  higher  and 
higher,  the  work  accumulates  in  the  form  of  potential  en- 
ergy. As  a  body  free  to  move  (i.e.  meeting  with  no  re- 
sistance) acquires,  under  the  influence  of  a  constant  force, 
uniformly  accelerated  motion,  so  does  work,  in  the  form 


104  WORK  AND  ENERGY. 

of  kinetic  energy,  accumulate.  But  accumulated  work  or 
energy  does  not  always  vary  as  the  work  performed.  In 
practice,  more  or  less  of  the  work  done,  especially  that 
done  in  overcoming  friction,  resistance  of  fluids,  etc.,  is 
wasted.  The  work  done  by  the  sawyer  and  bullet,  page 
102,  so  far  as  imparting  energy  to  the  bodies  on  which  they 
do  work,  is  all  lost.  Of  the  vast  amount  of  work  done  in 
propelling  a  steamer  across  the  ocean  none  accumulates ; 
all  is  wasted,  distributed  along  the  watery  path,  and  can- 
not be  recovered  or  made  available  for  doing  more  work. 
Evidently  the  accumulated  work  or  available  energy  that  a 
body  possesses  is  the  work  done  upon  the  body  less  the 
wasted  work.  We  may  then  calculate  in  foot-pounds  (or 
kilogram  meters)  according  to  formulas  (1)  or  (2),  page  99, 
the  work  performed  on  a  body,  and  from  this  deduct  the 
number  of  foot-pounds  wasted ;  the  remainder  is  the  num- 
ber of  foot-pounds  of  available  energy  that  is  imparted 
to  the  body. 

89.  Power  of  an  Agent  to  do  Work,  or  Rate  at 
which  an  Agent  can  do  Work. — -In  estimating  the  total 
amount  of  work  done,  the  time  consumed  is  not  taken 
into  consideration.  The  work  done  by  a  hod-carrier,  in 
carrying  1,000  bricks  to  the  top  of  a  building,  is  the  same 
whether  he  does  it  in  a  day  or  a  week.  But  in  estimating 
the  power  of  any  agent  to  do  work,  as  of  a  man,  a  horse, 
or  a  steam-engine,  in  other  words,  the  rate  at  which  it  is 
capable  of  doing  work,  it  is  evident  that  time  is  an  impor- 
tant element.  The  work  done  by  a  horse,  in  raising  a 
barrel  of  flour  20  feet  high,  is  about  4,000  foot-pounds ; 
but  even  a  mouse  could  do  the  same  amount  of  work  in 
time. 

The  unit  in  which  power  or  rate  of  doing  work  is  esti- 


METHODS   OF   ESTIMATING   WORK   AND   ENERGY.      105 

mated  is  called  (inappropriately)  a  horse-power.  A  horse- 
power represents  the  power  to  perform  33,000  foot-pounds  of 
work  in  a  minute  (or  550  foot-pounds  in  a  second). 

EXERCISES. 

1.  Can  a  person  lift  himself,  or  put  himself  in  motion,  without 
exerting  force  upon  some  other  body  ? 

2.  Can  a  body  do  work  upon  itself?    Can  a  body  generate  energy 
in  itself,  i.e.  increase  its  own  energy  ? 

3.  (a)  Suppose  that  an  average  force  of  25  pounds  is  exerted 
through  a  space  of  10  inches  in  bending  a  bow;  what  amount  of 
energy  will  it  give  the  bow  ?    (6)  What  kind  of  energy  will  the  bow, 
when  bended,  possess  ? 

4.  (a)  What  amount  of  kinetic  energy  does  a  body  weighing  20 
pounds,  and  moving  with  a  velocity  of  300  feet  per  second,  possess  ? 
(&)  What  amount  of  work  can  the  body  do  ? 

5.  (a)  What  amount  of  work  is  required  to  raise  50  tons  of  coal 
from  a  mine  200  feet  deep  ?     (6)  An  engine  of  how  many  horse-power 
would  be  required  to  do  it  in  two  hours  ? 

6.  How  many  fold  is  the  kinetic  energy  of  a  body  increased  by 
doubling  its  velocity? 

7.  Twelve  hundred  foot-pounds  of  energy  will  raise  100  pounds 
how  high,  if  none  is  wasted? 

8.  A  force  of  500  pounds  acts  upon  a  body  through  a  space  of  20 
feet.     One-fourth  of  the  work  is  wasted  in  consequence  of  resistances. 
How  much  available  energy  is  imparted  to  the  body  ? 

9.  How  much  energy  is  stored  in  a  body  weighing  1,000  pounds,  at 
a  hight  of  200  feet  above  the  earth  ? 

10.  How  much  work  can  a  2  horse-power  engine  do  in  an  hour  ? 

11.  A  horse  draws  a  carriage  on  a  level  road  at  the  uniform  rate 
of  5  miles  an  hour,     (a)  Does  work  accumulate  ?     (b)  What  kind  of 
energy  does  the  carriage  possess  ?    (c)  Suppose  that  the  carriage  were 
drawn  up  a  hill ;  would  energy  accumulate  ?    (W)  What  kind  of  energy 
would  it  possess  when  at  rest  on  the  top  of  the  hill  ?    (e)  How  would 
you  calculate  the  quantity  of  energy  it  possesses  when  at  rest  on  top 
of  the  hill  ?    (/")  Suppose  that  the  carriage  is  in  motion  on  top  of  the 
hill ;  what  two  formulas  would  you  employ  in  calculating  the  total 
energy  which  it  possesses  ? 


106  WORK   AND   ENERGY. 

Section   II. 

THE  ABSOLUTE  OR  C.G.S.  SYSTEM  OF  MEASUREMENTS. 

90.  Fundamental  Units.  — For  many  scientific  purposes,  espe- 
cially in  establishing  a  complete  set  of  electrical  units,  a  different  system 
for  measuring  physical   quantities  than  that  in  common  use  and  called 
the  gravitation  system,  is  indispensable.     In  the  new  system,  all  physical 
quantities  may  be  expressed  in  terms  of  three  units,  which  are  called  funda- 
mental units.   All  others  are  deduced  from  these  by  definition,  and  are  called 
derived  units.    The  fundamental  units  and  their  symbols  are  as  follows :  — 

Unit  of  length,  L :  the  centimeter,  or  the  hundredth  part  of  a  meter. 

Unit  of  mass,  M :  the  gram,  or  the  mass  of  one  cubic  centimeter  of 
distilled  water  at  4°  C. 

Unit  of  time,  T:  a  second. 

The  system  of  units  based  on  these  three  fundamental  units  is  called 
the  Absolute  System,  or  the  Centimeter-Gram-Second  System,  or,  by 
abbreviation,  C.G.S.  System. 

91.  Derived  Units.  —  There  are  a  great  number  of  derived  units. 
We  give  a  few  of  those  in  most  common  use. 

Unit  of  velocity,  V:  one  centimeter  per  second;  in  uniform  motion, 

v=«. 

T 

Unit  of  acceleration,  A :  an  increase  of  velocity  of  one  centimeter  per 
second. 

Unit  of  force,  F:  a  dyne,-  it  is  that  force  which,  acting  for  a  second, 
will  give  to  a  mass  of  one  gram  an  acceleration  of  one  centimeter  per 
second,  i.e.  one  unit  of  acceleration.  It  is  the  -  part  of  the  weight  of  the 
unit  of  mass.  ^ 

F  =  MA  =  — ,  or  MLT-2. 

T2 

Unit  of  work,  W ;  or  of  energy,  E :  an  erg ;  it  is  the  work  done  or 
energy  imparted  by  a  force  of  one  dyne  working  through  a  length  or 
distance  of  one  centimeter. 

W  or  E  =  FS  =  MAS  =  M-^,  or  ML2T~2. 

92.  Relation  of  the  Dyne  to  the  Gram  or  Gravitation 
Unit  of  Weight.  —  When  a  body  falls  in  a  vacuum,  gravity  imparts  to 


THE  ABSOLUTE  OR  C.G.S.  SYSTEM  OF  MEASUREMENTS.     107 

it  an  acceleration  of  g  (in  the  latitude  of  the  Northern  States,  980)  centi- 
meters per  second.  The  force  of  gravity,  therefore,  acting  on  a  unit  of 
mass  is,  according  to  definition,  g  (980)  dynes.  The  weight  of  a  mass  of 
one  gram  is  in  the  gravitation  system  one  gram.  Hence  the  gram  (gravi- 
tation unit  of  weight)  must  be  equal  to  g  dynes,  or,  in  the  Northern  United 
States,  to  980  dynes.  The  weight  of  a  mass  of  one  gram  varies  with  the 
latitude  and  hight  above  the  earth's  surface,  while  the  mass  of  a  gram  and 
the  dyne  are  constant  quantities;  their  value  does  not  change  with  place. 

93.  Another  Formula  for  Computing  Kinetic  Energy. 

—  It  is  evident  that  the  weight  of  a  body  is  dependent  upon  its  mass  and 
the  force  of  gravity  ;  in  other  words,  (W  =  M#)  the  weight  of  a  body  is 
measured  by  the  product  of  the  acceleration  which  the  force  of  gravity 
produces  into  its  units  of  mass.  Hence  the  mass  of  a  body  is  numerically 

_  its  weight.  Substituting  the  value  of  W  given  above  in  the  formula 
g 


(p.  103),  E  =        -,    we  have   E  =  When  the  latter  formula  is  used, 

it  is  evident  that  the  mass  of  the  moving  body  must  be  found  by  dividing 
its  weight  in  grams  by  980,  or  its  weight  in  pounds  by  32.1  +. 

The  absolute  system  is  used  in  all  refined  physical  measurements, 
but  the  gravitation  system  is  more  convenient  and  is  universally  used  in 
the  ordinary  affairs  of  life. 

QUESTIONS. 

[Designed  for  only  those  who  may  take  up  the  absolute  system.] 

1.  (a)  Name  some  unit  of  force  which  is  based  upon  the  weight  of 
some  definite  mass.     (6)  Name  some  unit  of  force  which  is  based  upon  the 
amount  of  acceleration  which  a  force  can  impart  to  a  body  of  a  given 
mass  in  a  given  time,     (c)  Have  both  of  these  units  absolute  (unchange- 
able) values?     (d)  What  names  do  you  employ  in  distinguishing  these 
two  classes  of  units  ? 

2.  (a)  What   are    the    fundamental  units   of   the  absolute    system? 
(6)  Why  are  they  called  fundamental  units  ? 

3.  A  force  of  20s  is  equivalent  to  how  many  dynes  ? 

4.  (a)  A  force  of  20  dynes  would  perform  how  many  ergs  of  work  in 
acting  through  a  distance  of  10cm  ?     (6)  How  many  ergs  of  work  would  a 
force  of  20  grams  perform  in  acting  through  the  same  distance  ?    (c)  How 
many  kilogrammeters  of  work  would  a  force  of  20  grams  perform  in  acting 
through  the  same  distance  ? 

5.  What  is  the  weight  of  a  mass  of  Is  in  dynes  ? 


108 


WOBK  AND  ENERGY. 


Section  III. 

MACHINES. 

94.   Uses  of  Machines. 

Experiment  74.  —  Suspend,  as  in  Figure  95,  a  fixed  pulley,  A,  and 
a  movable  pulley,  B.  The  scale-pan  C  counterbalances  the  pulley  B, 
so  that  there  will  be  equilibrium.  Suspend  from  B  two  balls,  LL,  of 
equal  weight,  and  suspend  on  the  side  where  the  pan  is,  a  single  ball, 

K,  equal  to  one  of  the  former.  The 
single  ball  supports  the  two  balls  ; 
i.e.  by  the  use  of  the  machine,  a  force 
of  1  is  enabled  to  balance  a  force  of 
2.  So  far  no  work  is  done.  (Why  ?) 
Place  a  very  small  weight  in  the  pan, 
and  the  balls  LL  begin  to  rise,  and 
work  is  done. 

As  the  weight  K  plus  a  very  small 
weight  causes  the  motion,  we  shall 
regard  this  as  the  force  (F)  ;  and  as 
the  weights  LL  are  the  bodies  moved 
(the  pulleys  and  pan  being  parts  of 
the  machine  may  be  disregarded), 
they  may  be  regarded  as  the  re- 
sistance (R)  overcome,  or  the  body 
on  which  work  is  done.  Measure 
the  respective  distances  through 
which  F  acts  and  R  moves  during 
the  same  time.  R  moves  only  one- 
half  as  great  a  distance  as  that  through  which  F  acts ;  i.e.  if  R  rises 
2  feet,  F  must  act  through  4  feet.  Suppose  that  R  is  2  pounds,  then 
F  is  1  +  pounds.  Now  2  (pounds)  X  2  feet  =  4  foot-pounds  of  work 
done  on  R.  Again,  1  +  (pounds)  X  4  feet  =  a  little  more  than  4  foot- 
pounds of  work  (or  energy)  expended. 

It  thus  seems  that,  although  a  machine  will  enable  a 
small  force  to  balance  a  large  force,  when  work  is  per- 


Fig.  95. 


MACHINES.  109 

formed,  the  work  applied  to  the  machine  is  greater,  rather 
than  less,  than  the  work  which  the  machine  transmits  to 
the  resistance.  The  work  applied  is  greater  than  the 
work  transmitted  by  the  amount  of  work  wasted  in  conse- 
quence of  friction  and  other  extra  resistances.  So  that 
by  the  employment  of  a  machine  nothing  is  gained  in  work 
which  the  force  is  required  to  do,  but  always  something  lost. 
What,  then,  is  the  advantage  gained  in  using  this 
machine?  Suppose  that  R  is  400  pounds,  and  that  the 
utmost  force  that  a  man  can  exert  is  a  little  more  than 
200  pounds.  Then,  without  the  machine,  the  services  of 
two  men  would  be  required  to  move  the  resistance; 
whereas  one  man  can  move  it  with  a  machine,  only  that 
he  will  be  obliged  to  move  twice  as  far  as  the  resistance 
moves,  a  matter  of  little  consequence  in  comparison  with 
the  advantage  of  being  able  to  do  the  work  alone.  The 
advantage  gained  in  this  instance  seems  to  be  one  of  con- 
venience. Men,  however,  are  accustomed  to  speak  of  it  as 
"  a  gain  of  force"  (or  more  commonly  and  inaccurately, 
"  of  power "),  inasmuch  as  a  small  force  overcomes  a 
large  resistance. 

Experiment  75.  —  If  instead  of  applying  the  small  additional 
weight  to  the  pan,  it  be  suspended  from  one  of  the  balls  LL,  the  weight 
of  these  balls,  together  with  the  additional  weight,  becomes  the  cause 
of  motion,  and  K  is  the  resistance.  In  this  case  there  is  a  loss  of 
force,  because  the  force  employed  is  more  than  twice  as  great  as  the 
force  overcome.  Measure  the  distances  traversed  respectively  by  F  and 
R  in  the  same  time.  R  moves  twice  as  far  as  F,  and  of  course  with 
twice  the  velocity.  There  is  a  gain  of  velocity  at  the  expense  of  force. 

It  thus  appears  that,  if  it  should  be  desirable  to  move  a 
resistance  with  greater  velocity  than  it  is  possible  or  con- 
venient for  the  force  to  act,  it  may  be  accomplished 
through  the  mediation  of  a  machine,  by  applying  to  it  a 


110 


WORK   AND   ENERGY. 


force  proportionally  greater  than  the  resistance.  This 
apparatus  is  one  of  many  contrivances  called  machines. 
A  machine  is  a  contrivance  for  transferring  or  transforming 
energy.  [Machines  for  transforming  energy  will  be  con- 
sidered in  future  chapters.]  Some  of  the  many  advan- 
tages derived  from  the  use  of  machines  are  :  — 

(1)  They  may  enable  us  to  exchange  intensity  of  force 
for  velocity,  or  velocity  for  intensity  of  force.  A  gain  of  in- 
tensity of  force  or  a  gain  of  velocity  is  called  a  mechani- 
cal advantage. 

They  may  enable  us  to  employ  a  force  in  a  direction 
more  convenient  than  the  direction  in  which  the  resist- 
to  be  moved. 

(3)  They  may  enable  us  to  employ  other 
forces  than  our  own  in  doing  work;  e.g. 
the  strength  of  animals ;  the  forces  of  wind, 
water,  steam,  etc. 

How  are  the  last  two  uses  illustrated  in 
Figure    96  ?      The    pulleys    employed   are 
called  fixed  pulleys,  i.e.  they  have  no  motion 
except  that  of  rotation.      Is  any  mechani- 
cal  advantage    gained    by    fixed    pulleys  ? 
What  is  the  use  of  a  fixed  pulley  ?     Pulley 
B  (Fig.  94)  is  a   movable  pulley.     What 
kind  of  advantage  is  gained  by 
means  of  a  movable  pulley  ? 


(2) 
that  is 
ance  is 


Fig.  96. 


95.  General  Law  of  Machines. 

—  From  the  experiments  and  dis- 
cussion above  we  derive  the  following  formula  for  r  ma- 
chines :  — 

FS  =  RS'  +  w, 


MACHINES.  Ill 

in  which  F  represents  the  force  applied,  and  S  the  distance 
through  which  F  acts ;  R  represents  the  resistance  over- 
come, and  S'  the  distance  through  which  its  point  of  ap- 
plication is  moved  ;  w  represents  the  wasted  work.  A 
machine  in  which  there  is  no  wasted  work  is  a  perfect 
machine.  Such  a  machine  is  purely  ideal,  as  none  exists. 
If  in  our  calculations  we  regard  a  machine  as  perfect 
(though  subsequently  suitable  allowance  must  be  made 
for  the  wasted  work),  then  our  formula  becomes 

FS  -  RS'. 

Whence  R  :  F  : :  S  :  S' ;  i.e.  the  force  and  resistance  vary 
inversely  as  the  distances  which  their  respective  points  of  ap- 
plication move.  In  other  words,  the  ratio  of  the  resistance 
to  the  force  is  the  reciprocal  of  the  ratio  of  the  distances 
which  these  points  move. 

R:F  =  4,  then  S':S  =  J. 

This  law  applies  to  every  machine  of  whatever  descrip- 
tion ;  hence  it  is  called  the  G-eneral  or  Universal  Law  of 
Machines.  When  R  is  greater  than  F,  there  is  a  gain  of 

r> 

force,   and  —  =  the  ratio   of  gain  of  force.     When  S;  is 


F 


S 


greater  than  S,  there  is  a  gain  of  velocity,  and  "^r  =  the 
ratio  of  gain  of  velocity. 

Experiment  76.  —  Support  a  lever,  as  in  Figure  97,  so  that  there 
shall  be  unequal  arms.  Move  w  until  the  lever  is  balanced  in  a  hori- 
zontal position.  Suspend  (say) 
seven  balls  from  the  short  arm 
(say)  one  space  from  the  ful- 
crum. Then  from  the  other 
arm  suspend  a  single  ball  from 
such  a  place  (in  this  case  seven 
equal  spaces  from  the  fulcrum) 
that  it  will  balance  the  seven 
balls.  There  is  now  equilibrium  between  the  two  forces.  Suppose 


112 


WORK   AND   ENERGY. 


the  smaller  force  to  be  increased  a  little  and  to  produce  motion  ;  what 
mechanical  advantage  (i.e.  intensity  of  force  or  velocity)  would  be 
gained  by  the  use  of  the  machine  ?  What  is  the  ratio  of  gain  neg- 
lecting the  small  additional  force?  How  does  this  ratio  compare  with 
the  ratio  between  the  length  of  the  two  arms  ?  For  convenience  we 
call  the  distance  of  the  point  of  application  of  the  force  from  the 
fulcrum  the  force-arm,  and  the  distance  of  the  resistance  from  the 
fulcrum  the  resistance-arm. 

Suppose  the  small  additional  force  is  applied  to  the  short  arm; 
what  mechanical  advantage  would  be  gained  ?  What  would  be  the 
ratio  of  gain  ? 

While  the  general  law  of  machines  is  always  applica- 
ble, a  special  law,  one  in 
which  the  relation  be- 
tween the  ratio  of  gain 
and  the  ratio  between 
certain  dimensions  of 
the  machine  is  stated,  is 
often  more  convenient  in 
practice.  For  example, 
in  our  experiment  with 
the  lever  we  discover 
that  R  :  F  : :  force-arm  : 
resistance-arm,  i.e.  the 
force  and  resistance  vary 
inversely  as  the  lengths 
of  their  respective  arms. 
Compare  this  special  law 
with  the  general  law. 
Place  the  fulcrum  at  other  points  in  the  lever,  and  thereby 
vary  the  length  of  the  arms,  and  verify  by  numerous 
experiments  the  special  law  of  levers. 

Experiment  77.  —  By  means  of  a  pulley,  D,  so  arrange  (Fig.  98) 
that  both  F  and  R  may  be  on  the  same  side  of  the  fulcrum.  First, 


Fig.  98. 


MACHINES. 


113 


place  in  the  pan  weights  sufficient  to  produce  equilibrium  in  the 
machine  (for  example,  in  this  case,  one  ball).  Then  suspend  weights 
at  some  point,  as  A,  and  place  other  weights  in  the  pan  to  counter- 
balance these.  Verify  the  law  of  levers.  If  A  is  the  resistance,  what 
mechanical  advantage  is  gained  ?  What  is  the  ratio  of  gain  ?  If  B 
is  the  resistance,  what  mechanical  advantage  will  be  gained  ? 

Experiment  78. — Obtain 
a  toy  carriage,  place  it  on  an 
inclined  plane,  pass  the  cord 
over  a  pulley,  B  (Fig.  99), 
so  adjusted  that  the  cord 
between  the  carriage  and 
pulley  shall  be  parallel  with 
the  plane.  Suspend  a  small 
bucket,  P,  and  place  sand  in 
it  to  balance  the  carriage. 
Place  in  the  carriage  a  weight  W,  and  place  weights  in  the  bucket  to 
balance  W.  The  weights  placed  in  the  bucket  represent  the  force 


Fig.  99. 


Fig.  loo.  Fig.  un- 

applied ;  then  what  advantage  is  gained  in  the  use  of  an  inclined  plane 
as  a  machine?  W,  in  traversing  the  inclined  plane  AB,  only  rises 
through  the  vertical  hight  CB,  while  P  must  move  through  a  distance 
equal  to  AB.  Measure  the  distances  AB  and  CB.  How  does  the  ratio 


114 


WORK   AND   ENERGY. 


between  these  distances  compare  with  the  ratio  of  gain  ?     Construct  a 
special  law  of  the  inclined  plane. 

Experiment  79.  —  Place  a  "wheel  and  axle"  (Fig.  100)  on  the 
support  A.  Wind  a  cord  around  the  wheel  B,  and  another  in  the  re- 
verse direction  around  the  axle  C.  Suspend  a  weight,  D,  from  the 
axle,  and  another,  E,  from  the  wheel,  to  balance  it.  If  E  be  the 
force  applied,  what  advantage  is  gained  ?  What,  if  D  is  the  force 
applied  ?  What  is  the  ratio  of  advantage  in  either  case  ?  How  does 
the  ratio  of  advantage  compare  with  the  ratio  between  the  radius  of 
the  wheel  AC  (Fig.  101)  and  the  radius  of  the  axle  BC  ?  Construct  a 
special  law  of  the  wheel  and  axle  . 


Fig.  102. 
EXERCfSES. 

1.  (a)  When  is  a  machine  said  to  gain  intensity  of  force?    (b)  When 
is  it  said  to  gain  velocity  V 


MACHINES. 


115 


2.  (a)  Can  any  machine  do  work  ?     (6)  Can  we  by  the  use  of  any 
machine  accomplish  more  work  than  the  work  performed  upon  the 
machine  ?    What  is  the  proof  ? 

3.  How  is    intensity  of    force 
gained  by  the  use  of  a  machine  ? 

4.  What  machine  is  used  only 
to  change  the  direction  of  motion  ? 

5.  (a)  What  is  a  mechanical 


Fig.  1O3. 

(6)  Give  a  rule  by  which   the  mechanical   advantage 


Fig.  104. 


advantage  ? 

that  may  be  gained  by  any  machine  may  be  calculated. 

6.  Figure  102  repre- 
sents a  pile-driver,  (a) 
How  can  the  energy  or 
the  work  which  the  weight 
W  can  do  when  it  is  raised 
a  given  distance  be  com- 
puted ?  (b)  What  benefit  is  derived  from  the  use  of  the  machine  in 
raising  the  weight  ?  (c)  Suggest  some  simple  attachment  to  the 
machine  which  would  enable  one  man  to  raise  the  weight,  (e?)  Sug- 
gest some  attachment  by  means  of  which  a  horse  could  be  made  to  do 
the  work,  (e)  What 
difference  will  it  make 
whether  the  weight  is 
raised  5  feet  or  10 
feet?  (/)  Illustrate, 
by  means  of  this  ma- 
chine, what  you  un- 
derstand by  force  and 
energy.  (g}  Which, 
while  the  weight  rises, 
is  constantly  accumu- 
lating, and  which  re- 


Fig.  105. 


mains  nearly  constant  ? 
(A)  Which  can  be  meas- 
ured with  an  instrument,  and  what  is  the  name  of  the  instrument? 

7.  (a)  What  advantage  is  gained  by  a  lever  when  its  force-arm  is 
longer  thin  its  resistance-arm?     (b)  What,  when  its  resistance-arm  is 
longer? 

8.  (a)  What  advantage  is  gained  by  a  nut-cracker  (Fig.   103)? 
(6)  What  is  the  ratio  of  gain  ? 


116 


WORK  AND   ENERGY. 


Fig.  106. 


9.  (a)  What  advantage  is  gained  by  cutting  far  back  on  the  blades 
of  shears  near  the  fulcrum?  Why?  (b)  Should  shears  for  cutting 
metals  be  made  with  short  handles  and  long  blades,  or  the  reverse  ? 
(c)  What  is  the  advantage  of  long  blades  ? 

10.  Is  work  done  when  the 
moment  of  the   force  applied 
to  a  lever  is  equal  to  the  mo- 
ment of  the  resistance  ?  Why  ? 

11.  (a)   If    P   (Fig.   105), 
weighing  1  pound,  is  suspend- 
ed 15  spaces  from  the  fulcrum 
of  the  steelyard,  what  weight 
(W),    suspended     3     similar 
spaces  the    other  side  of  the 
fulcrum,  will  balance  it  ?     (&) 

Where  would  you  place  the  one-pound  weight  in  order  to  weigh  out 
6  pounds  of  tea? 

12.  (a)  If  the  circumference  of  the  axle  (Fig.  106)  is  15  inches, 
and  the  force  applied  to  the  crank  acts  through  15  feet  during  each  rev- 
olution, what  force  will  be  necessary 

to  raise  the  bucket  of  coal  weighing 
(say)  36  pounds?  (b)  Through  how 
many  feet  must  the  force  act  to  raise 
the  bucket  from  a  cavity  48  feet 
deep? 

13.  The  arm  is  raised  by  the  con- 
traction   (shortening    by    muscular 
force)  of  the  muscle  A  (Fig.  107), 
which  is  attached  at  one  extremity 
to  the  shoulder  and  at  the  other  ex- 
tremity B  to  the  fore-arm,  near  the 

elbow,  (a)  When  the  arm  is  used,  as  represented  in  the  figure,  to 
raise  a  weight,  what  kind  of  a  machine  is  it  ?  (b)  What  mechanical 
advantage  is  gained  by  it  ?  (c)  How  can  the  ratio  of  gain  be  com- 
puted ?  (c?)  For  which  purpose  is  the  arm  adapted,  to  gain  intensity 
of  force  or  velocity  ? 

The  lengths  of  the  two  arms  of  a  balance,  such  as  is  used  in  finding 
specific  gravity  (Fig.  60,  page  61),  should  be  exactly  equal.  The  arms 
may  be  of  unequal  length,  and  yet  the  beam  may  be  in  equilibrium 


Fig.  107. 


MACHINES. 


117 


(i.e.  take  a  horizontal  position  when  no  weights  are  applied),  in  conse- 
quence of  having  more  matter  in  the  shorter  arm,  as  in  Figure  97,  page 
111.  Such  a  balance  is  called  a,  false  balance. 

14.  (a)  How  would  you  test  a  balance  to  ascertain  whether  it  is 
true  or  false  ?  (6)  If  you  were  buying  diamonds,  and  the  seller  should 
sell  them  to  you  by  weight  as  obtained  by  placing  them  on  the  shorter 
arm  of  a  false  balance,  would  you  be  the  loser  or  gainer? 

The  true  weight  of  a  body  may  be  found  with  a  false  balance  by  a 
process  called  double  weighing.  The  article  to  be  weighed  is  placed  in  one 
pan,  and  a  counterpoise  of  sand  in  the  other  pan.  The  article  is  then 
removed,  and  known  weights  placed  in  the  pan  until  equilibrium  is  again 
produced.  These  weights  represent  the  correct  weight  of  the  article.  In 
this  way  the  balances  used  in  the  school  laboratory  should  be  tested  by 
the  pupil 


Fig.  1O8. 


Fig.  109. 


15.  During  one  revolution   a  screw  advances  a  distance  equal  to 
the  distance  between  two  threads,  measured  in  the  direction  of  the 
axis  of  the  screw.     Suppose  the  screw  in  the  letter-press  (Fig.  108)  to 
advance  \  inch  at  each  revolution,  and  a  force  of  25  pounds  to  be 
applied  to  the  circumference  of  the  wheel  B,  whose  diameter  is  14 
inches.    What  pressure  would  be  exerted  on  articles  placed  beneath 
the  screw?     (The  circumference  of  a  circle  is  3.1416  times  its  diame- 
ter.) 

16.  The  toggle-joint  (Fig.  109)  is  a  machine  employed  where  great 
pressure  has  to  be  exerted  through  a  small  space,  as  in  punching  and 


118 


WORK   AND   ENERGY. 


Fig.  110. 


shearing  iron,  and  in  printing-presses,  in  pressing  the  types  forcibly 

against  the  paper.  An  illustration 

may  be  found  in  the  joints  used  to 

raise  carriage-tops.   Force  applied 

to  the  joint  C  will  cause  the  two 

links  AC  and  BC  to  be  straight- 
ened, or  carried  forward  to  e.    If 

point  C  moves  5  inches  while  G 

moves  |  inch,  then  what  pressure 

will  a  force  of  50  pounds  applied 

at  C  exert  on  the  book  below  ? 
17.  Show  that  the  hydrostatic 

press  (page  50)  conforms  in  its 
operation  to  the  general  law  of  machines. 

18.  A  wedge  may  be  regarded  as  two  inclined 
planes  placed  base  to  base,   as  dc   (Fig.  110). 

(a)  What  mechanical  advantage  is  gained  by  it  ? 

(b)  Suppose  that  the  thickness  db  is  4  inches, 
and  the  length  dc  is  8  inches,  and  that  the  aver- 
age pressure  exerted  upon  it  by  the  blow  of  a 
sledge  is  100  pounds ;  what  will  be  the  average 
pressure  exerted  by  the  wedge  tending  to  separate 
the  fibers  of  wood  ? 

A  compound  machine  is  one  consisting  of  two  or  more  machines 

combined  in  one;  e.g.  com- 
pound pulleys  (Fig.  Ill)  and 
compound  wheels  and  axles 
(Fig.  112).  The  mechanical 
advantage  that  may  be  gained 
by  a  compound  machine  may 
be  calculated  by  multiplying 
continuously  together  the  ra- 
tios of  the  several  machines. 

19.  (a)    How  great  is  the 
advantage  gained  by  one  mov- 
able pulley?   (b)  How  great  is 
the  advantage  gained  by  the 
Fig.  113.  compound  pulley   (Fig.   Ill) 

consisting  of  three  movable  pulleys? 


MACHINES. 


119 


20.  Suppose  that  the  radii  of  the  wheels  «,  d,  and/  (Fig.  112)  are, 
respectively,  20  inches,  16  inches,  and  24  inches,  and  the  radii  of  their 
axles  are,  respectively,  2  inches,  4  inches,  and  6  inches;  how  great 
advantage  may  be  gained  by  the  compound  machine? 


Fig.  113. 


21.  How  would  you  calculate  the  mechanical  advantage  gained  by 
a  machine  like  that  of  Figure  113  ?    (On  the  axle  A  is  an  endless  screw, 
by  means  of  which  motion  is  communicated  from  the  axle  to  the 
wheel  W.) 

22.  (a)  What  kind  of  a  machine  is  a  claw-hammer  (Fig.  114)? 
(6)  What  mechanical  advantage  is  gained  by  it  ? 

23.  In  its  technical  meaning,  a  "  perpetual  motion  machine  "  is  not 
a  machine  that  will  run  indefinitely,  but  a  machine  which  can  do  work 
without  the  expenditure  of  energy.     Is  such  a  machine  possible? 

24.  A  plank  12  feet  long  and  weighing  24  pounds  is  supported  by 
two  props,  one  3  feet  from  one  end,  and  the  other  1  foot  from  the 
other  end.     What  is  the  pressure  on  each  prop? 

25.  With  a  movable  pulley  what  force  will  support  a  weight  of 
100  pounds  ? 

26.  The  gradient  of  a  certain  road  on  a  hillside  is  one  foot  in  ten 
feet.     What  force  must  a  horse  exert  on  a  carriage  which  weighs  to- 
gether with  its  load  one  ton,  to  prevent  its  descent  ? 

27.  What  must  be  the  diameter  of  a  wheel  in  order  that  a  force  of 
20  pounds  a,pplied  at  its  circumference  may  be  in  equilibrium  with  a 
resistance  of  600  pounds  applied  to  its  axle,  which  is  3  inches  in  diam- 
eter? 


120  WORK    AND    ENERGY. 

28.  Draw  a  straight  line  to  represent  a  lever ;  locate  the  fulcrum, 
and  locate  the  points  of  application  of  the  force  and  resistance  un- 
equally distant  from  the  fulcrum.  Draw  lines  from  the  points  of 
application  of  the  force  and  resistance  so  that  they  will  make  some 
angle  with  each  other  (i.e.  not  parallel  with  each  other)  to  represent 
the  directions  in  which  the  two  forces  respectively  act.  Ascertain  the 
ratio  between  the  two  forces  when  their  moments  are  equal,  i.e.  when 
the  two  forces  are  in  equilibrium. 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSICS 

* 

CHAPTER  V. 
MOLECULAR   ENERGY.  — HEAT. 

Section  I. 

WHAT   HEAT   IS. — SOME   SOURCES   OF   HEAT. 

96.  Theory  of  Heat.  —  A  body  loses  motion  in  com- 
municating it.  The  hammer  descends  and  strikes  the 
anvil;  its  motion  ceases,  but  the  anvil  is  not  sensibly 
moved ;  the  only  observable  effect  produced  is  heat.  In- 
stead of  a  motion  of  the  hammer  and  anvil,  there  is  now, 
according  to  the  modern  view,  an  increased  vibratory  mo- 
tion of  the  molecules  that  compose  the  hammer  and  anvil, 
—  simply  a  change  from  molar  to  molecular  motion.  Of 
course,  this  latter  motion  is  invisible.  According  to  this 
view,  heat  is  but  a  name  for  the  energy  of  vibration  of  the 
molecules  of  a  body.  A  body  is  heated  by  having  the 
motion  of  its  molecules  quickened,  and  cooled  by  parting 
with  some  of  its  molecular  motion.  One  body  is  hotter 
than  another  when  the  average  kinetic  energy  of  each  mole- 
cule in  it  is  greater  than  in  the  other. 

As  late  as  the  beginning  of  the  present  century  heat  was  generally 
regarded  as  " a  sensation  which  the  presence  of  fire "  (an  " igneous  fluid" 
"  matter  of  heat,"  called  sometimes  "  caloric  ")  "  occasions  in  animate  and 
inanimate  bodies."  A  text-book  of  that  period  makes  this  significant 
statement :  "There  is  fire  in  the  wood,  and  there  is  air  in  the  field,  though 
we  do  not  perceive  either  while  at  rest.  Kubbing  two  pieces  of  wood  does 
not  create  fire  any  more  than  the  blowing  of  the  wind  creates  air.  Motion 
renders  both  perceptible."  The  former  and  the  more  modern  views  are  in 


122          MOLECULAR  ENERGY. — HEAT. 

harmony  in  attributing  the  immediate  cause  of  the  sensation  to  motion. 
According  to  the  former  view,  the  sensation  is  produced  by  putting  an 
imaginary  fluid  in  motion ;  according  to  the  modern  view  it  is  produced  by 
quickening  the  motion  of  the  molecules  of  a  body. 

97.  Artificial  Sources  of  Heat.  —  As  heat  is  energy, 
so  all  heat  must  originate  in  some  form  of  energy,  i.e.  by 
the  transformation  of  some  other  form  of  energy  into  heat. 

Experiment  80.  —  Place  a  ten-penny  nail  on  a  stone  or  a  flat 
piece  of  iron  and  hammer  it  briskly  for  a  few  minutes.  It  soon  be- 
comes too  hot  to  be  handled  with  comfort.  Rub  a  desk  with  your  fist ; 
your  coat-sleeve  with  a  metallic  button;  both  the  rubbers  and  the 
things  rubbed  become  heated. 

(1)  Heat  is  generated  at  the  expense  of  molar  motion, 
i.e.  molar  motion  checked  becomes  molecular  motion,  or  heat. 

Experiment  81.  —  Take  a  glass  test-tube  half  full  of  cold  water 
and  pour  into  it  one-fourth  its  volume  of  strong  sulphuric  acid.  The 
liquid  almost  instantly  becomes  so  hot  that  the  tube  cannot  be  held  in 
the  hand. 

When  water  is  poured  upon  quicklime,  heat  is  rapidly 
developed.  The  invisible  oxygen  of  the  air  combines  with 
the  constituents  of  the  various  fuels,  such  as  wood,  coal,, 
oils,  and  illuminating-gas,  and  gives  rise  to  what  we  call 
burning,  or  combustion,  by  which  a  large  amount  of  heat  is 
generated.  In  all  such  cases  the  heat  is  generated  by  the 
combination  or  clashing  together  of  molecules  of  sub- 
stances that  have  an  affinity  (i.e.  an  attraction)  for  one 
another.  Before  union  the  energy  of  the  molecules  is  of 
the  same  kind  as  that  of  a  stone  on  a  shelf.  When  the 
shelf  is  withdrawn,  gravity  converts  the  potential  energy 
of  the  stone  into  kinetic  energy ;  so  affinity  converts  the 
potential  energy  of  the  molecules  into  kinetic  energy 
of  vibration ;  i.e.  into  heat. 


WHAT   HEAT   IS.  123 

(2)  Molecular  (or  atomic)  potential  energy  is  transformed 
in  the  act  of  chemical  combination  into  heat. 

98.    The  Sun  as  a  Source  of  Heat  and  Energy.  —  The 

sun  is  the  source  of  very  nearly  all  the  energy  employed  by 
man  in  doing  work.  Our  coal-beds,  the  results  of  the  de- 
posit of  vegetable  matter,  are  vast  storehouses  of  the  sun's 
energy,  rendered  potential  during  the  growth  of  the  plants 
many  ages  ago.  The  animal  finds  its  food  in  the  plant, 
appropriates  the  energy  stored  in  the  plant,  and  converts 
it  into  energy  of  motion  in  the  form  of  animal  heat  and 
muscular  motion.  Every  rain-drop  that  rolls  its  way  to  the 
sea,  contributing  its  mite  to  the  immense  water-power  of 
the  earth,  derives  its  energy  from  the  sun. 

QUESTIONS. 

1.  On  every  hand  we  see  what   appears  to  be  at  least  an  almost 
universal  tendency  to  destruction   of   motion.      Is   the   destruction 
usually  an  annihilation  of  motion  ? 

2.  What  name  is  usually  given  to  molecular  energy? 

3.  How  does  it  appear  that  heat  is  energy? 

4.  What  do  you  mean  when  you  say  that  one  body  is  hotter  than 
another  ? 

5.  How  must  all  heat  originate  ? 

6.  State  all  the  sources  of  heat  with  which  you  are  now  acquainted. 

7.  (a)  Give  an  illustration  of  mechanical  or  visible  motion  trans- 
formed into  molecular  motion.     (6)  Give  an  illustration  of  molecular 
motion  transformed  into  mechanical  motion. 

8.  What  kind  of  energy  does  coal  and  other  fuel  possess  ? 

9.  A  lump  of  coal  is  raised  and  placed  upon  a  shelf,     (a)  How  can 
the  potential  energy  of  the  lump  be  transformed  into  kinetic  energy  ? 
(6)  Will  the  kinetic  energy  resulting  from  the  transformation   be 
mechanical  or  molecular  ?     (c)  When  the  lump  strikes  the  earth,  what 
transformation  of  energy  occurs  ? 

10.  Every  lump  of  coal  possesses  molecular  potential  energy,     (or) 
How  can  its  energy  be  transformed  into  kinetic  energy  ?     (6)  What 


124  MOLECULAR    ENERGY. — HEAT. 

two  varieties  of  potential  energy  does  a  lump  of  coal  on  the  shelf 


11.  (a)  How  do  bodies  acquire  energy?     (b)  From  what  source  did 
coal  obtain  its  molecular  potential  energy  ?     (c)  What  does  the  entire 
value  of  coal  consist  in? 

12.  How  does  animal  energy  originate  ? 


Section  II. 

TEMPERATURE.  —  METHODS   OF   EQUALIZATION. 

99.  Temperature    Defined.  —  If   body  A   is   brought 
in   contact  with   body  B,  and   A   tends   to   impart   heat 
to  B,  then  A  is  said  to  have  a  higher  temperature  than 
B.      Temperature  is  the  state  of  a  body  with  reference  to 
its  tendency  to  communicate  heat  to,  or  receive  heat  from, 
other  bodies.      The  direction  of  the  flow  of  heat  deter- 
mines which  of  two  bodies  has  the  higher  temperature. 
If  the  temperature  of  neither  body  rises  at  the  expense 
of  the  other,  then  both  have  the  same  temperature. 

100.  Temperature  distinguished  from  Quantity  of 
Heat.  —  The  term  temperature  does  not  signify  quantity 
of  heat.    If  we  dip  from  a  gallon  of  boiling  water  a  cupful, 
the  cup  of  water  is  just  as  hot,  i.e.  has  the  same  tempera- 
ture, as  the  larger  quantity,  although  of  course  there  is  a 
great  difference  in  the  quantities  of  heat  the  two  bodies  of 
water  contain.     Temperature  depends  upon  the  average  ki- 
netic energy  of  the  individual  molecule,  while  quantity  of 
heat  depends  upon  the  average  kinetic  energy  of  the  indi- 
vidual molecule  multiplied  by  the  number  of  molecules. 


TEMPERATURE.  —  METHODS   OF   EQUALIZATION.      125 

There  is  always  a  tendency  to  equalization  of  tempera- 
ture; that  is,  heat  has  a  tendency  to  pass  from  a  warmer 
body  to  a  colder,  or  from  a  warmer  to  a  colder  part  of  the 
same  body,  until  there  is  an  equality  of  temperature. 

1O1.    Conduction. 

Experiment  82.  —  Place  one  end  of  a  wire  about  10  inches  long 
in  a  lamp-flame,  and  hold  the  other  end  in  the  hand.  Heat  gradually 
travels  from  the  end  in  the  flame  toward  the  hand.  Apply  your  fin- 
gers successively  at  different  points  nearer  and  nearer  the  flame ;  you 
find  that  the  nearer  you  approach  the  flame,  the  hotter  the  wire  is. 

The  flow  of  heat  through  an  unequally  heated  body, 
from  places  of  higher  to  places  of  lower  temperature,  is 
called  conduction  ;  the  body  through  which  it  travels  is 
called  a  conductor.  The  molecules  of  the  wire  in  the  flame 
have  their  motion  quickened ;  they  strike  their  neighbors 
and  quicken  their  motion ;  the  latter  in  turn  quicken  the 
motion  of  the  next ;  and  so  on,  until  some  of  the  motion 
is  finally  communicated  to  the  hand,  and  creates  in  it  the 
sensation  of  heat. 

Experiment  83.  —  Figure  115  represents  a  board  on  which  are 
fastened,  by  means  of  staples,  four  wires :  (1) 
iron,  (2)  copper,  (3)  brass,  and  (4)  German 
silver.  Place  a  lamp-flame  where  the  wires  meet. 
In  about  a  minute  run  your  fingers  along  the 
wires  from  the  remote  ends  toward  the  flame, 
and  see  how  near  you  can  approach  the  flame  on 
each  without  suffering  from  the  heat.  Make  a 
list  of  these  metals,  arranging  them  in  the  order  Fis-  H5- 

of  their  conduetibility. 

You  learn  that  some  substances  conduct  heat  much  more 
rapidly  than  others.  The  former  are  called  good  conduc- 
tors, the  latter  poor  conductors.  Metals  are  the  best  con- 
ductors, though  they  differ  widely  among  themselves. 


MOLECULAR    ENERGY.  —  HEAT. 


Experiment  84. —  Fill  a  test-tube  full  of  water,  and  hold  it  some- 
what inclined  (Fig.  116),  so  that  a  flame  may  heat  the  part  of  the 
tube  near  the  surface  of  the  water.  Do 
not  allow  the  flame  to  touch  the  part  of 
the  tube  that  does  not  contain  water. 
The  water  may  be  made  to  boil  near  its 
surface  for  several  minutes  before  any 
change  of  the  temperature  at  the  bottom 
will  be  perceived. 

Liquids,  as   a   class,  are  poorer 
conductors  than  solids.     Gases  are 
Fig.  lie.  much  poorer  conductors  than  liquids. 

It  is  difficult  to  discover  that  pure,  dry  air  possesses  any 
conducting  power.  The  poor  conducting  power  of  our 
clothing  is  due  partly  to  the  poor  conducting  power  of 
the  fibers  of  the  cloth,  but  chiefly  to  the  air  which  is 
confined  by  it. 

Loose  garments,  and  garments  of  loosely  woven  cloth,  inasmuch  as 
they  hold  a  large  amount  of  confined  air,  furnish  a  good  protection  from 
heat  and  cold.  Bodies  are  surrounded  with  bad  conductors,  to  retain  heat 
when  their  temperature  is  above  that  of  surrounding  objects,  and  to 
exclude  it  when  their  temperature  is  below  that  of  surrounding  objects. 
In  the  same  manner  double  windows  and  doors  protect  from  cold. 


1O2.    Convection  in  Gases. 

Experiment  85.  —  Hold  your  hand  a  little  way 
from  a  flame,  beneath,  on  the  side  of,  and  above  the 
flame.  At  which  place  is  the  heat  most  intense  ? 

Experiment  86.  —  Draw  on  thin  glazed  paper 
an  unfolding  line,  so  that  the  windings  shall  be 
about  |  inch  apart.  Cut  along  the  line;  give  the 
central  portion  a  conical  form ;  place  the  cone  on 
a  pointed  end  of  a  vertical  wire,  and  allow  the 
remainder  of  the  paper  to  fall  spirally  around  the 
wire  as  in  Figure  117.  Place  the  spiral  over  a  flame 
or  hot  stove.  A  continuous  current  of  air,  a  mini- 


Fig.  117. 


ature  wind,  moving  upward  from  the  flame  or  stove  causes  the  spiral 


TEMPERATURE.  —  METHODS   OF   EQUALIZATION.     127 

to  rotate.  This  current  tends  only  upward.  The  air  having  become 
heated  by  contact  with  the  surfaces  of  the  flame  or  stove  conveys,  in 
its  ascent,  heat  to  objects  above.  Heat  is  thus  diffused  by  a  process 
called  convection  (conveying). 

Experiment  87.  —  Cover  a  candle-flame  with  a  glass  chimney  (Fig. 
118),  blocking  the  latter  up  a  little  way  so  that  there  may  be  a  circu- 
lation of  air  beneath.  Hold  the  spiral  over  the  chimney;  the  rotation 
is  much  quicker  than  before.  Hold  smoking  touch-paper  near  the 
bottom  of  the  chimney;  the  smoke  seems  to  be  drawn  with  great 
rapidity  into  the  chimney  at  the  bottom ;  in  other  words,  the  office  of 
the  chimney  is  to  create  what  is  called  a  draft  of  air.  Notice  whether 
the  combustion  takes  place  any  more  rapidly  with  than  without  the 
chimney. 


Fig.  118.  Fig.  119. 

Experiment  88.  —  Place  a  candle  within  a  circle  of  holes  cut  in  the 
cover  of  a  vessel,  and  cover  it  with  a  chimney,  A  (Fig.  119).  Over 
an  orifice  in  the  cover  place  another  chimney,  B.  Hold  a  roll  of 
smoking  touch-paper  over  B.  The  smoke  descends  this  chimney, 
passes  through  the  vessel  and  out  at  A.  This  illustrates  the  method 
often  adopted  to  produce  a  ventilating  draft  through  mines.  Let  the 
interior  of  a  tin  vessel  represent  a  mine  deep  in  the  earth,  and  the 
chimneys  two  shafts  sunk  to  opposite  extremities  of  the  mine.  A  fire 
kept  burning  at  the  bottom  of  one  shaft  will  cause  a  current  of  air 


128 


MOLECULAR  ENERGY.  —  HEAT. 


to  sweep  down  the  other  shaft,  and  through  the  mine,  and  thus  keep 
up  a  circulation  of  pure  air  through  the  mine. 

The  cause  of  the  ascending  currents  is  evident.  Air,  on  becoming 
heated,  expands  rapidly  and  becomes  much  rarer  than  the  surround- 
ing colder  air ;  hence  it  rises  much  like  a  cork  in  water,  while  cold 
air  pours  in  laterally  to  take  its  place.  In  this  manner  winds  are 
created. 

The  so-called  trade-winds  originate  in  the  torrid  or  heated  zone  of  the 
earth.  The  air  over  the  heated  surface  of  the  earth  rises,  and  the  colder 
air  from  the  polar  regions  flows  in  on  both  sides,  giving  rise  to  a  constant 
southward  wind  in  the  northern  hemisphere,  and  northward  wind  in  the 
southern  hemisphere. 

Chemistry  teaches  us  the  vital 
importance  of  thorough  ventilation. 
Figure  120  represents  a  scheme  for 
heating  a  room  by  steam,  and  venti- 
lating it  by  convection.  Steam  is 
conveyed  by  a  pipe  from  the  boiler 
to  a  radiator  box  just  beneath  the 
floor  of  the  room.  The  air  in  the 
box  becomes  heated  by  contact  with 
and  radiation  from  the  coil  of  pipe 
in  the  box,  and  rises  through  a  pas- 
sage opening  by  means  of  a  register 
into  the  room  near  the  floor  at  C,  a 
supply  of  pure  air  being  kept  up  by 
means  of  a  tubular  passage  opening 
into  the  box  from  the  outside  of 
the  building.  Thus  the  room  is  fur- 
nished with  pure  warm  air,  which, 
mingling  with  the  impurities  aris- 
ing from  the  respiration  of  its  occu- 
pants, serves  to  dilute  them,  and 
render  them  less  injurious.  At  the 
same  time,  the  warm  and  partially 
Fig.  120.  vitiated  air  of  the  room  passes 

through  the  open  ventilator,  A,  into  the  ventilating-flue,  and  escapes,  so 
that  in  a  moderate  length  of  time  a  nearly  complete  change  of  air  is 
effected.  It  is  evident  that  on  the  coldest  days  of  winter  the  convection 
is  most  rapid ;  indeed,  it  may  be  so  rapid  that  the  air  cannot  be  heated 
sufficiently  to  render  the  room  neai1  the  floor  comfortable.  At  such  times 


TEMPERATURE. — METHODS   OF   EQUALIZATION.     129 

the  ventilator  A  may  be  closed,  while  the  ventilator  B  is  always  open. 
The  heated  air  rises  to  top  of  the  room  and,  not  being  able  to  escape, 
crowds  the  colder  air-  beneath  out  at  the  ventilator  B.  No  system  of 
ventilation  dependent  wholly  on  convection  is  adequate  to  ventilate 
properly  crowded  halls ;  air  is  too  viscous  and  sluggish  in  its  movements. 
In  such  cases  ventilation  should  be  assisted  by  some  mechanical  means, 
such  as  a  blower  or  fan,  worked  by  steam  or  water  power. 

103.  Convection  in  Liquids. 

Experiment  89.  —  Fill  a  small  (6  ounce),  thin  glass  flask  with 
boiling  hot  water,  color  it  with  a  teaspoonful  of  ink,  stopper  the  flask, 
and  lower  it  deep  in  a  tub,  pail,  or  other  large  vessel  rilled  with  cold 
water.  Withdraw  the  stopper,  and  the  hot,  rarer,  colored  water  will 
rise  from  the  flask,  and  the  cold  water  will  descend  into  the  flask. 
The  two  currents  passing  in  and  out  of  the  nack  of  the  flask  are  easily 
distinguished.  The  colored  liquid  marks  distinctly  the  path  of  the 
heated  convection  currents  through  the  colored  liquid  and  makes  clear 
the  method  by  which  heat,  when  applied  at  the  bottom  of  a  body  of 
liquid,  becomes  rapidly  diffused  through  the  entire  mass  notwithstand- 
ing that  liquids  are  poor  conductors. 

Experiment  90.  —  Fill  again  the  flask  with  hot  colored  water, 
stopper,  invert,  and  introduce  the  mouth  of  the  flask  just  beneath  the 
surface  of  a  fresh  pail  of  cold  water.  Withdraw  the  stopper  with  as 
little  agitation  of  the  water  as  possible.  What  happens?  Explain. 

104.  Radiation. —  In  some  way  the  sun  is  the  cause 
of  a  large  amount  of  the  heat  which  -the  surface  of  the 
earth  possesses.     On  the  other  hand,  the  earth  in  some 
way   parts   with  a  large    amount  of   heat.      It   is   quite 
apparent  that  the  earth  does  not  receive  heat  from  the 
sun  by  conduction   or   convection,   and    that   by  neither 
of   these   processes   does  it  part  with   heat.      It  is  also 
apparent  that  there  is  another  and  a  much  more  rapid 
and  effectual  method  by  which  bodies  of  higher  tempera- 
ture on  the  earth  part  with  their  heat,  and  other  bodies  of 
lower  temperature  acquire  heat  at  the  expense  of  distant 
bodies,  than  by  either  of  the  two  comparatively  slow  pro- 
cesses of  diffusion  so  far  described.     This  process  is  called 


130  MOLECULAR   ENERGY.  —  HEAT. 

radiation.  The  process  is  a  very  peculiar  one,  and  must 
be  reserved  for  discussion  in  its  proper  place  in  the  chapter 
on  Radiant  Energy. 

QUESTIONS. 

1.  Why  does  more  heat  reach  your  hand  above  than  at  an  equal 
distance  beside  a  flame  ? 

2.  Why  is  loose  clothing  warmer  than  tight-fitting  clothing? 

3.  (a)  Which  contains  more  heat,  the  Atlantic  Ocean  or  a  tea-kettle 
full  of  boiling  water?     (6)  Which  is  capable  of  giving  heat  to  the 
other?    (c)  Can  a  body  have  less  heat  than  another  and  yet  be  hotter 
than  the  other? 

4.  Why  should  heat  be  applied  to  the  bottom  of  a  body  of  water? 

5.  (a)  How  is  equalization  of  temperature  effected  in  solids?    (6)  In 
liquids  and  gases  ? 


Section  III. 

EFFECTS  OF   HEAT. — EXPANSION. 

1O5.   Expansion  of  Solids,  Liquids,  and  Gases. 

Experiment  91. —  The  brass  ring  and  ball  (Fig.  121)  are  so 
constructed  that  the  latter  will  just  pass  through 
the  former  when  both  have  the  same,  or  nearly  the 
same,  temperature.  Heat  the  ball  quite  hot  in  a 
flame,  and  ascertain  by  trying  to  pass  it  through  the 
ring  whether  it  has  increased  in  size.  Devise  some 
method  of  passing  it  through  the  ring  without  cooling 
the  ball. 

Experiment  92. —  Figure   122  represents  a  thin 
Fig.  121.        brass  plate  and  an  iron  plate  of  the  same  dimensions 
riveted  together  so  far  as  to  form  what   is  called  a  compound  bar. 
Place  the  bar  edgewise  in  a  flame,  dividing  the  flame  in  halves  (one- 


EFFECTS  OF  HEAT.  —  EXPANSION.  131 

half  on  each  side  of  the  bar)  so  that  both  metals  may  be  equally 
heated.  The  bar,  which  was  at  first  straight,  is  now  bent,  owing  to 
the  unequal  expansion  of  the  two  metals  on  receiving  equal 
increments  of  heat.  Which  metal  expands  more  rapidly? 
Thrust  the  hot  bar  into  cold  water.  What  happens  ?  Cover 
the  bar  with  chips  of  ice.  What  happens? 

Experiment  93.  —  Fit  stoppers  (perforated  rubber  stop- 
pers are  best)  tightly  in  the  necks  of  two  similar  thin 
glass  flasks  (or  test-tubes),  and  through  each  stopper  pass 
a  glass  tube  about  18  inches  long.  The  flasks  should  be 
nearly  of  the  same  size.  Fill  one  flask  with  water  and  the 
other  with  alcohol,  and  crowd  in  the  stoppers  so  as  to  force 
the  liquids  up  the  tubes  a  little  way  above  the  stoppers. 
Set  both  flasks  at  the  same  time  into  a  large  basin  of  hot  Fig7"i22. 
water  in  order  that  both  may  have  the  same  opportunity  to 
acquire  heat.  Soon  the  liquids  begin  to  expand  and  rise  in  the 
tubes.  Which  liquid  is  more  expansible  ? 

Experiment  94.  — Take  a  dry  flask  like  that  used  in  Experiment 
89,  insert  the  end  of  the  tube  in  a  bottle  of 
colored  water  (Fig.  123),  and  apply  heat  to  the 
flask ;  the  enclosed  air  expands  and  comes  out 
through  the  liquid  in  bubbles.  After  a  few 
minutes,  withdraw  the  heat,  keeping  the  end 
of  the  tube  in  the  liquid ;  as  the  air  left  in  the 
flask  cools,  it  loses  some  of  its  tension,  and 
the  water  is  forced  by  atmospheric  pressure  up 
the  tube  into  the  flask,  and  partially  fills  it.  ^ 

Experiment  95.  —  Partly  fill  a  foot-ball  (see 
Fig.  9,  page  8)  with  cold  air,  close  the  orifice, 
and  place  it  near  a  fire.  The  air  will  expand 
and  distend  the  ball. 

Different  substances,  both  in  the  solid 
and  liquid  states,  expand  unequally  on  Flg' 

experiencing  equal  changes  of  temperature.  Except  at 
very  low  temperatures,  all  gases  expand  alike  for  equal 
changes  of  temperature.  Under  uniform  pressure  (as  is 
very  nearly  the  case  in  the  experiment  with  the  balloon) 


132  MOLECULAB    ENERGY.  —  HEAT. 


the  volume  of  any  body  of  gas  varies  -^  its  volume  at 
the  freezing-point  of  water  for  every  degree  Centigrade, 
or  -jiy  for  every  degree  Fahrenheit,  its  temperature  is 
changed.  But  if  the  gas  is  confined  in  a  vessel  of  rigid 
sides,  so  that  its  volume  is  necessarily  constant,  then 
its  tension  varies  in  the  same  ratio  for  every  degree  its 
temperature  is  changed. 

The  force  exerted  by  bodies  in  expanding  or  contracting  is  very  great, 
as  shown  by  the  following  rough  calculation  :  If  an  iron  bar,  1  square  inch 
in  section,  is  raised  from  0°  C.  (freezing-point  of  water)  to  500°  C.  (a  dull, 
red  heat),  its  length,  if  allowed  to  expand  freely,  will  be  increased  from 
1  to  1.006.  Now,  a  force  capable  of  stretching  a  bar  of  iron  of  1  square 
inch  section  this  amount  is  about  90  tons,  which  represents  very  nearly  the 
force  that  would  be  necessary  to  prevent  the  expansion  caused  by  heat. 
It  would  require  an  equal  force  to  prevent  the  same  amount  of  contraction 
if  the  bar  is  cooled  from  500°  to  0°  C. 

Boiler  plates  are  riveted  with  red-hot  rivets,  which,  on  cooling,  draw  the 
plates  together  so  as  to  form  very  tight  joints.  Tires  are  fitted  on  carriage- 
wheels  when  red  hot,  and,  on  cooling,  grip  them  with  very  great  force. 

1O6.   Abnormal  Expansion  and  Contraction  of  Water. 

—  Water  presents  a  partial  exception  to  the  general  rule 
that  matter  expands  on  receiving  heat  and  contracts  on 
losing  it.  If  a  quantity  of  water  at  0°  C.,  or  32°  R,  is 
heated,  it  contracts  as  its  temperature  rises,  until  it  reaches 
4°  C.,  or  about  39°  F.,  when  its  volume  is  least,  and  there- 
fore it  has  its  maximum  density.  If  heated  beyond  this 
temperature,  it  expands,  and  at  about  8°  C.  its  volume  is 
the  same  as  at  0°.  On  cooling,  water  reaches  its  maximum 
density  at  4°  C.,  and  expands  as  the  temperature  falls 
below  that  point.  [See  treatment  of  Expansion-Coeffi- 
cients, Section  E,  Appendix.] 


THERMOMETRY.  133 

Section  IV. 

THERMOMETRY. 

A  thermometer  primarily  indicates  changes  in  volume ; 
but  as  changes  of  volume  are  caused  by  changes  of  tem- 
perature, it  is  commonly  used  for  the  more  important  pur- 
pose of  indicating  temperature. 

1C 7.  Construction  of  a  Thermometer.  —  A  thermom- 
eter generally  consists  of  a  glass  tube  of  capillary  bore, 
terminating  at  one  end  in  a  bulb.  The  bulb  and  part  of 
the  tube  are  filled  with  mercury,  and  the  space  in  the  tube 
above  the  mercury  is  usually  a  vacuum.  On  the  tube,  or 
on  a  plate  behind  the  tube,  is  a  scale  to  show  the  hight  of 
the  mercurial  column. 

108.  Standard  Temperatures.  —  That  a  thermometer 
may  indicate  any  definite  temperature,  it  is  necessary  that 
its  scale  should  relate  to  some  definite  and  unchangeable 
points  of  temperature.     Fortunately  nature  furnishes  us 
with  two  convenient  standards.     It  is  found  that  under 
ordinary  atmospheric  pressure  ice   always   melts   at    the 
same  temperature,  called  the  melting-point,  or,  more  com- 
monly, the  freezing-point  (water  freezes  and  ice  melts  at 
the  same  temperature).     Again,  the  temperature  of  steam 
rising  from  boiling  water  under  the  same  pressure  is  always 
the  same. 

109.  Graduation  of  Thermometers.  —  The  bulb  of  a 
thermometer  is  first  placed  in  melting  ice  (Fig.  124),  and 
allowed  to  stand  until  the  surface  of  the  mercury  becomes 


134 


MOLECULAR  ENERGY.  —  HEAT. 


stationary,  arid  a  mark  is  made  upon  the  stem  at  that 
point,  and  indicates  the  freezing-point.  Then  the  instru- 
ment is  suspended  in  steam  rising  from  boiling  water  (Fig. 
125),  so  that  all  but  the  very  top  of  the  column  is  in  the 
steam.  The  mercury  rises  in  the  stem  until  its  tempera- 
ture becomes  the  same  as  that  of  the  steam,  when  it  again 
becomes  stationary,  and  another  mark  is  placed  upon  the 
stem  to  indicate  the  boiling-point.  Then  the  space  be- 


Fig.  134. 


Fig.  125. 


tween  the  two  points  found  is  divided  into  a  convenient 
number  of  equal  parts  called  degrees,  and  the  scale  is  ex- 
tended above  and  below  these  points  as  far  as  desirable. 

Two  methods  of  division  are  adopted  in  this  country : 
by  one,  this  space  is  divided  into  180  equal  parts,  and  the 
result  is  called  the  Fahrenheit  scale,  from  the  name  of  its 
author ;  by  the  other,  the  space  is  divided  into  100  equal 
parts,  and  the  resulting  scale  is  called  centigrade,  which 
means  one  hundred  steps.  In  the  Fahrenheit  scale,  which 
is  generally  employed  in  English-speaking  countries  for 
ordinary  household  purposes,  the  freezing  and  boiling 


THERMOMETRY. 


135 


points  are  marked  respectively  32°  and  212°. 
The  0  of  this  scale  (32°  below  freezing- 
point),  which  is  about  the  lowest  tempera- 
ture that  can  be  obtained  by  a  mixture  of 
snow  and  salt,  was  incorrectly  supposed  to 
be  the  lowest  temperature  attainable.  The 
centigrade  scale,  which  is  generally  em- 
ployed by  scientists,  has  its  freezing  and 
boiling  points  more  conveniently  marked, 
respectively  0°  and  100°.  A  temperature  be- 
low 0°  in  either  scale  is  indicated  by  a  minus 
sign  before  the  number.  Thus  —  12°  F.  in- 
dicates 12°  below  0°  (or  44°  below  freezing- 
point),  according  to  the  Fahrenheit  scale. 

To  reduce  a  Fahrenheit  reading  to  a 
centigrade  reading,  first  subtract  32  from 
the  given  number,  and  then  multiply  by  ^. 
Thus, 


100c 


To  change  a  centigrade  reading  to  a  Fah- 
renheit reading,  first  multiply  the  given 
number  by  -|,  and  then  add  32.  Thus, 

Fig.  126. 

11O.  Absolute  Zero. —  The  zeros  on  the  thermometric 
scales  which  we  have  hitherto  considered  are  provisional, 
arbitrary.  Absolute  zero  is  the  temperature  corresponding 
to  total  absence  of  heat.  At  the  absolute  zero  the  mole- 
cules must  be  supposed  to  be  at  rest.  At  this  temperature 
gases  (if  they  may  be  called  such)  exert  no  pressure,  and 
occupy  no  space  save  that  which  their  molecules  take  up 
when  closely  packed  together.  The  point  of  absolute  zero 
is  a  point  beyond  which  no  cooling  is  conceivable.  It  is 
independent  of  the  conventions  of  man. 


136          MOLECULAR  ENERGY. HEAT. 

Now  it  has  been  found  that  the  pressure  in  air  increases 
or  diminishes  by  .00367  =  (about)  ^^  of  its  pressure  at 
0°  for  each  centigrade  degree  of  rise  or  fall  of  temperature, 
the  volume  being  maintained  constant.  If  air  were  a  per- 
fect gas,  and  could  be  cooled  down  in  this  way  to  —  273° 
C.  ( — 459.4°  F.),  it  would  exert  no  pressure.  The  reason 
it  would  exert  no  pressure  is  that  its  particles  possess  no 
kinetic  energy,  no  motion.  This  is  assumed,  therefore,  to 
be  the  absolute  zero  of  temperature. 

111.  Absolute  Temperature.  —  Absolute  temperature 
is  that  reckoned  from  the  absolute  zero,  or  — 273°  C. 
Temperatures  measured  from  absolute  zero  are  proportional 
to  the  pressure  of  a  theoretically  perfect  gas  of  constant 
volume  or  density. 

The  absolute  temperature  (based  on  the  above  theory) 
of  any  body  is  found  by  adding  273  to  its  temperature  as 
indicated  by  a  centigrade  thermometer,,  or  459.4  to  its 
temperature  as  indicated  by  a  Fahrenheit  thermometer. 

EXERCISES. 

1.  Express  the  following  temperatures  of  the  centigrade  scale  in  the 
Fahrenheit  scale:  100°;  40°;  56°;  60°;  0°;  -20°;   -40°;  80°;  150. 

NOTE.  —  In  adding  or  subtracting  32°,  it  should  be  done  algebraically. 
Thus  to  change  —14°  C.  to  its  equivalent  on  the  Fahrenheit  scale  :  f  X 
(—  14)  =  —  25.2°;  —  25.2°  +  32°  =  6.8°,  the  required  temperature  on  the 
Fahrenheit  scale.  Again,  to  find  the  equivalent  of  24°  F.  in  the  centi- 
grade scale  :24  —  32=— 8;— 8X  f  =  —  4f  ;  hence,  24°  F.  is  equivalent 
to  -  4.4°  +  C. 

2.  Express  the  following  temperatures  of  the  Fahrenheit  scale  in 
the  centigrade  scale  :  212°;  32°;  90°;  77°;  20°;  10°;  -  10°;  -  20°; 
-40°;  40°;  59°;  329°. 

3.  Mercury  freezes  at  —  39°  C.  and  boils  at  350°  C.;  find,  in  both 
centigrade  and  Fahrenheit  degrees,  the   absolute   temperatures   at 
which  mercury  freezes  and  boils. 


LIQUEFACTION   AND   VAPORIZATION.  137 


Section  V. 

EFFECTS  OF  HEAT  CONTINUED.  —  LIQUEFACTION   AND 
VAPORIZATION. 

112.  Liquefaction.  —  As  previously  stated  (page  9), 
whether  a  body  exist  in  a  solid,  liquid,  or  gaseous  state 
depends  upon  its  temperature  and  the  pressure  which  it  is 
under. 

Experiment  96. —  Take  a  lump  of  ice  as  large  as  your  two  fists, 
put  it  into  boiling  water ;  when  reduced  to  about  \  its  original  size 
skim  it  out.  Wipe  the  lump,  and  place  one  hand  on  it  and  the  other 
on  a  lump  to  which  heat  has  not  been  applied.  Do  you  perceive  any 
difference  in  their  temperatures?  Ice  reduces  the  temperature  of 
victuals  in  our  refrigerators ;  do  the  victuals  raise  the  temperature  of 
the  ice?  How  does  the  heat  which  the  victuals  impart  to  the  ice 
affect  it? 

Experiments  and  experience  teach  that  (1)  the  melting 
or  solidifying  point  (they  are  always  the  same  for  the  same 
substance)  may  vary  widely  for  different  substances,  but 
for  the  same  substance  it  is  invariable  when  under  the  same 
pressure. 

(2)  The  temperature  of  a  solid  or  liquid  remains  con- 
stant at  the  melting-point  from  the  moment  that  melting  or 
solidification  begins. 

113.    Vaporization. 

Experiment   97.  —  Place   a  test-tube    (Fig.    127), 
half  filled  with  ether,  in  a  beaker  containing  water  at 
a  temperature  of  60°  C.     Although  the  temperature  of 
the  water  is  40°  below  its  boiling-point,  it  very  quickly 
raises  the  temperature  of  the  ether  sufficiently  to  cause 
Fig.  137.       it  to  boil  violently.    Introduce  a  chemical  thermometer1 
into  the  test-tube,  and  ascertain  the  boiling-point  of  ether. 

1  A  chemical  thermometer  has  its  scale  on  tho  glass  stem,  instead  of  a  plate,  and  is 
otherwise  adapted  to  experimental  use. 


138 


MOLECULAR  ENERGY. HEAT. 


Experiment  98.  —  Take  two  beakers  half  full  of  water.  Kaise 
both  to  the  boiling-point.  Dissolve  pulverized  saltpetre  in  one  as 
long  as  it  readily  dissolves.  Suspend  in  both  liquids  chemical  ther- 
mometers, so  that  the  bulb  of  each  shall  be  within  one  inch  of  the 
bottom.  Does  the  boiling  water,  as  you  continue  to  apply  heat,  get 
hotter?  Is  the  boiling  solution  any  hotter  than  the  boiling  water? 
Does  the  solution  get  hotter  as  it  becomes  concentrated  by  loss  of 
water  by  vaporization  ? 

After  a  liquid  begins  to  boil,  the  temperature  remains  con- 
stant until  the  whole  is  vaporized,  if  the  density  of  the  liquid 
and  the  pressure  remain  constant. 

Experiment  99.  —  Place  a  beaker,  half  full  of  water  at  80°  C., 
under  the  receiver  of  an  air-pump,  and  exhaust  the  air.  The  water, 
though  far  below  its  usual  boiling-point,  boils  violently.  Readmit  the 
air,  and  test  the  temperature  of  the  water  which  has  just  been  boiling. 


Fig.  138.  Fig.  129. 

Experiment  100.  —  Half  fill  a  thin  glass  flask  with  water.  Boil 
the  water  over  a  Bunsen  burner;  the  steam  will  drive  the  air  from 
the  flask.  Withdraw  the  burner,  quickly  cork  the  flask  very  tightly, 
invert  the  flask,  and  pour  cold  water  upon  the  part  containing  steam, 
as  in  Figure  128 ;  the  water  in  the  flask,  though  cooled  several  degrees 


LIQUEFACTION   AND  VAPORIZATION.  139 

below  the  usual  boiling-point,  boils  again  violently.  The  application 
of  cold  water  to  the  flask  condenses  some  of  the  steam,  and  diminishes 
the  tension  of  the  rest,  so  that  the  pressure  upon  the  water  is  dimin- 
ished, and  the  water  boils  at  a  reduced  temperature. 

If  hot  water  is  poured  upon  the  flask,  the  water  ceases  to  boil. 
Why? 

Experiment  101.  —  Provide  a  tumbler  of  cold  water,  a  test-tube 
nearly  filled  with  water,  tightly  stoppered,  and  having  glass  tubes  ex- 
tending through  the  stopper,  as  represented  in  Figure  129.  Place  the 
exposed  end  of  the  bent  tube  in  the  tumbler  of  water,  and  apply  heat  to 
the  bottom  of  the  test-tube,  and  boil  the  water  for  about  five  minutes. 
Then  remove  the  heat,  leave  the  end  of  the  tube  in  the  tumbler  of 
water,  and  allow  the  water  of  the  test-tube  to  cool  for  some  time  ;  or, 

better,   to  hasten  the 

d\\\  cooling,  place  the  test- 

tube  in  another  tum- 
bler of  cold  water.  Ob- 
serve carefully,  and 
explain  all  phenomena 
which  occur  from  the 
beginning  to  the  end 
of  the  operation. 

114.   Distillation. 

Experiment  102.  — 
Vessel  A  (Fig.  130) 
•(called  a  condenser) 
contains  a  coil  (called 
a  worm)  of  copper 
Fig'  130>  tube,  terminating  at 

one  extremity  at  a.  The  other  end  of  the  tube,  b,  projects  through 
the  side  of  the  vessel  near  its  bottom.  Near  the  top  of  the  vessel 
projects  another  tube,  c  (called  the  overflow),  with  which  is  con- 
nected a  rubber  tube,  e.  This  tube  conveys  the  warm  water  which 
rises  from  the  surface  of  the  heated  worm  away  to  a  sink  or  other 
convenient  receptacle. 

Take  a  glass  flask  of  a  quart  capacity,  fill  it  three-fourths  full  of  pond 
or  bog  water.  Connect  the  flask  by  means  of  a  glass  delivery-tube  with 
the  extremity  a  of  the  worm.  Heat  the  water  in  the  flask ;  as  soon  as 


140  MOLECULAR    ENERGY.  —  HEAT. 

it  begins  to  boil,  commence  siphoning  cold  water  through  a  small  tube, 
d,  from  an  elevated  vessel  E  into  the  condenser.  Inasmuch  as  the  worm 
is  constantly  surrounded  with  cold  water,  the  steam  on  passing  through 
it  becomes  condensed  into  a  liquid,  and  the  liquid  (called  the  distillate} 
trickles  from  the  extremity  b  into  a  receiving  vessel.  The  distillate 
is  clear,  but  the  water  in  the  flask  acquires  a  yellowish  brown  tinge 
as  the  boiling  progresses,  due  to  the  concentration  of  impurities 
(largely  of  vegetable  matter)  which  are  held  in  suspension  and  solu- 
tion in  ordinary  pond  water.  The  apparatus  used  is  called  a  still,  and 
the  operation  distillation. 

When  a  volatile  liquid  is  to  be  separated  from  water,  for  example, 
when  alcohol  is  separated  from  the  vinous  mash  after  fermentation  (see 
Chemistry,  page  184),  the  mixed  liquid  is  heated  to  its  boiling-point,  which 
is  lower  than  that  of  water.  Much  more  of  the  volatile  liquid  will  be  con- 
verted into  vapor  than  of  the  water,  because  its  boiling  point  is  lower. 
Thus  a  partial  separation  is  effected.  By  repeated  distillations  of  the 
distillate,  a  95  per  cent  alcohol  is  obtained. 

115.  Evaporation.  —  In  boiling,  the  heat,  applied  at 
the  bottom,  rapidly  converts  the  liquid  into  vapor,  which, 
rising  in  bubbles  and  breaking  at  or  near  the  surface,  pro- 
duces a  violent  agitation  in  the  liquid,  called  boiling  or 
ebullition.  Boiling  takes  place  only  at  a  definite  tempera- 
ture, which  depends  on  the  kind  of  liquid  and  the  pressure 
that  is  on  it.  Evaporation  is  that  form  of  vaporization 
which  takes  place  quietly  and  slowly  at  the  surface.  Al- 
though hastened  by  heat,  the  evaporation  of  water  occurs 
at  any  temperature,  however  low;  even  ice  and  snow 
evaporate. 

The  rapidity  of  evaporation  increases  with  the  tempera- 
ture, amount  of  surface  exposed,  dryness  of  the  atmosphere, 
and  diminution  of  pressure.  This  vapor  of  water  mixes 
freely  with  the  air,  and  diffuses  rapidly  through  it,  acting 
like  another  gas.  A  given  space,  —  for  example,  a  cubic 
foot  (it  matters  little  whether  there  is  air  in  the  space  or 
whether  it  is  a  vacuum),  can  hold  only  a  limited  amount 


LIQUEFACTION   AND   VAPORIZATION.  141 

of  water  vapor.  This  quantity  depends  on  the  tempera- 
ture of  the  vapor.  The  capacity  of  a  space  for  water 
vapor  increases  rapidly  with  the  temperature,  being  nearly 
doubled  by  a  rise  of  10°  C.  When  a  space  contains  sucli 
an  amount  of  water  vapor  that  it£  temperature  cannot  be 
lowered  without  some  of  the  water  being  precipitated  in 
the  form  of  a  liquid,  the  vapor  is  said  to  be  saturated, 
and  the  temperature  at  which  this  happens  is  called  the 
dew-point. 

Experiment  103.  —  Take  a  bright  nickel-plated  cup,  such,  for  ex- 
ample, as  are  used  for  lemonade-shakers ;  pour  into  it  a  small  quantity 
of  tepid  water.  Place  in  the  water  the  bulb  of  a  chemical  thermome- 
ter. Gradually  reduce  the  temperature  of  the  water  by  stirring  into 
it  ice  water  until  you  discover  a  slight  dimness  of  the  luster  of  that 
portion  of  the  outside  of  the  cup  next  the  water.  If  the  ice  water 
does  not  reduce  the  temperature  sufficiently,  add  ice,  keeping  the  mix- 
ture briskly  stirring.  If  the  ice  does  not  answer,  pour  out  some  of 
the  water  and  sprinkle  salt  on  the  ice,  keeping  the  bulb  of  the  ther- 
mometer in  the  remaining  water.  Note  the  temperature  of  the  water 
at  the  instant  that  the  first  mist  or  dimness  appears  on  the  cup. 
Wait  until  the  dimness  or  mist  disappears,  and  note  the  temperature 
of  the  water  when  the  last  disappears.  Take  the  mean  of  the  two 
temperatures  for  the  dew-point. 

The  form  in  which  the  condensed  vapor  appears  is,  according  to  its 
location,  dew,  fog,  or  cloud.1  The  atmosphere  is  said  to  be  dry  or  humid, 
not  according  to  the  quantity  of  water  vapor  which  it  at  any  time  contains, 
but  according  as  it  can  contain  much  or  little  more  than  it  has.  The  air 
in  summer  months  usually  contains  a  large  amount  of  water  vapor,  yet  it 
is  usually  very  dry.  The  heat  of  a  stove  dries  the  air  of  a  room  without 
destroying  any  of  its  water  vapor.  In  such  a  room,  the  lips,  tongue, 
throat,  and  skin  experience  a  disagreeable  sensation  of  dryness,  owing  to 
the  rapid  evaporation  which  takes  place  from  their  surfaces.  This  should 
be  taken  as  nature's  admonition  to  keep  water  in  the  stove  urns,  and 
tanks  connected  with  furnaces. 

1  A  cloud  is  simply  a  fog  in  an  elevated  region  of  the  atmosphere.  It  is  composed  of 
minute  spheres  of  water  from  7^53  to  TO\jC  of  an  inch  in  diameter. 


142  MOLECULAR    ENERGY. HEAT. 


Section  VI. 

HEAT  CONVERTIBLE  INTO   POTENTIAL   ENERGY,  AND   VICE 

VERSA. 

116.  Heat  Units.  —  It  is  frequently  necessary  to  meas- 
ure quantity  of  heat,  and  for  this  purpose  a  standard  unit 
of  measurement  is  required.  The  heat  unit  generally 
adopted  is  the  amount  of  heat  required  to  raise  the  tempera- 
ture of  one  kilogram  of  water  from  4°  to  5°  C.  This  unit  is 
called  a  calorie,  or  kilogram-centigrade. 

Let  it  be  required  to  find  approximately  the  amount  of 
heat  that  disappears  during  the  melting  of  one  kilogram 
of  ice. 

Experiment  104.  — Weigh  out  200«  of  dry  (dry  it  with  a  towel) 
ice  chips  whose  temperature  in  a  room  of  ordinary  temperature  may 
be  safely  assumed  to  be  0°  C.  Weigh  out  200&  of  boiling  water,  whose 
temperature  we  assume  to  be  100°  C.  Pour  the  hot  water  upon  the 
ice,  and  stir  until  the  ice  is  all  melted.  Test  the  temperature  of  the 
resulting  liquid. 

Suppose  its  temperature  is  found  to  be  10°  C.  It  is  evident  that 
the  temperature  of  the  hot  water  in  falling  from  100°  to  90°  would 
yield  sufficient  heat  to  raise  an  equal  weight  of  water  from  0°  to  10° 
C.  Hence  it  is  clear  that  the  heat  which  the  water  at  90°  yields  in 
falling  from  90°  to  10°  -—  a  fall  of  80°  —  in  some  manner  disappears. 
At  this  rate  had  you  used  lk  of  ice  and  lk  of  hot  water,  the  amount  of 
heat  lost  would  be  80  calories.  Careful  experiments,  in  which  suit- 
able allowances  are  made  for  loss  or  gain  of  heat  by  radiation  and 
conduction,  have  determined  that  80  calories  of  heat  are  consumed  in 
melting  1  kilogram  of  ice.  How  near  to  this  do  the  results  of  your  ex- 
periments approach  ? 

Next  let  it  be  required  to  find  the  amount  of  heat  that  disappears 
during  the  conversion  of  1  kilogram  of  water  into  steam. 

Experiment  105.  —  Take  in  a  porcelain  evaporating-dish  50g  of 


HEAT  CONVERTIBLE  INTO  POTENTIAL  ENERGY.      143 

ice  water  at  (say)  5°  C.  Place  it  over  a  flame,  and,  watch  in  hand, 
note  the  time  in  seconds  which  elapses  before  it  boils.  Then  note 
the  time  which  elapses  before  it  is  all  converted  into  steam.  Suppose 
that  it  required  100  seconds  to  raise  the  water  from  5°  to  its  boiling- 
point,  which  we  assume  is  100°  —  a  rise  of  95° ;  and  that  it  requires 
530  seconds  to  convert  the  water,  after  it  commences  to  boil,  into 
steam.  Then  the  latter  operation  consumes  (530-^100=)  about  5.3 
times  as  much  time  as  the  former.  But  the  heat  applied  to  the  water 
while  boiling  does  not  raise  its  temperature  (see  Exp.  98,  page  137) ; 
then  all  the  heat  given  to  the  water  during  the  interval  of  time  dis- 
appears. Had  you  taken  lk  of  water,  it  would  have  required  95  calo- 
ries to  raise  the  water  from  5°  to  100°  C.  Hence,  in  converting  the 
lk  of  water  into  steam,  95x5.3=  (about)  503  calories  disappear. 
Accurate  methods  have  determined  that  537  calories  disappear  during 
the  conversion  of  lk  of  water  into  steam. 

The  heat  which  disappears  in  melting  and  boiling  is 
generally,  but  with  our  present  knowledge  of  the  subject, 
rather  objectionably,  called  latent  (hidden)  heat.  The 
error  consists  in  calling  that  heat  which  has  ceased  to  be 
heat.  The  heat,  i.e.  kinetic  energy,  that  disappears  in 
melting  is  consumed  in  doing  interior  (i.e.  molecular)  work. 
The  molecules  that  in  the  solid  are  held  firmly  in  their 
places  by  molecular  forces,  are  moved  from  their  places 
during  melting,  and  so  work  is  done  against  these  forces, 
much  as  work  is  done  against  gravity  when  a  stone  is 
raised.  In  both  cases  kinetic  energy  is  consumed — disap- 
pears ;  but  this  means  simply  that  it  is  transformed  into 
potential  energy.  The  so-called  latent  heat  is  simply  a 
misnomer  for  molecular  potential  energy. 

When  water  is  converted  into  steam,  the  larger  portion  of  the  heat, 
which  is  rendered  latent,  is  consumed  in  separating  the  molecules  so  far 
that  molecular  attraction  is  no  longer  sensible ;  a  small  portion  —  about 
x1^ — is  consumed  in  overcoming  atmospheric  pressure.  The  amount  of 
work  done  in  melting  and  boiling  —  especially  the  latter  —  is  very  great, 
as  shown  by  the  amount  of  heat  consumed.  Hence  it  requires  a  long  time 
to  acquire  the  requisite  amount  of  heat.  This  is  a  protection  against 


144         MOLECULAR  ENERGY. — HEAT. 

sudden  changes.  For  example,  if  snow  and  ice  melted  immediately  on 
reaching  the  melting-point,  all  the  snow  and  ice  would  melt  in  a  single 
warm  day  in  winter,  creating  most  destructive  freshets. 

117.  Potential  Energy  converted  into  Heat  by  the 
Solidification  of  Liquids  and  the  Liquefaction  of 
Vapors.  —  If  our  theory  be  true  that  heat  is  converted 
into  potential  energy  during  vaporization  and  melting, 
then  ought  the  energy  to  be  restored  to  the  kinetic  state 
(i.e.  the  heat  which  disappears  during  these  operations 
ought  to  be  restored)  when  the  molecules  return  to  their 
original  positions,  i.e.  when  vapor  becomes  liquid,  or  when 
liquids  solidify. 

Experiment  106.  — Take  in  a  beaker  C  (Fig.  131)  lk  of  water  at 
(say)  12°  C.  Take  about 
500s  of  water  in  a  flask  A, 
and  raise  it  to  the  boiling- 
point.  As  soon  as  it  be- 
gins to  boil,  connect  the 
flask  with  the  beaker  by 
a  delivery-tube  B,  carry- 
ing the  end  of  the  tube 
nearly  to  the  bottom  of  the 
beaker.  When  about  one- 
fifth  of  the  water  has  boiled 
away,  remove  the  delivery 
tube  from  C,  and  immedi-  Flg*  131" 

ately  test  the  temperature  of  the  water  in  the  beaker,  and  weigh  it. 
Assume  that  the  temperature  of  the  steam  is  100°  C.,  and  we  will 
suppose,  for  illustration,  that  there  are  1,100=  of  water  now  in  the 
beaker;  then  100s  of  water  have  been  converted  into  steam  which 
has  passed  into  the  beaker  and  been  condensed  or  liquefied  by  the 
cold  water.  Suppose,  again,  that  the  •  temperature  of  the  water 
in  the  beaker  was  raised  thereby  to  70°  C.  Now  100*  of  water  at 
100°  C.  (resulting  from  the  condensation  of  the  steam)  in  falling  to 
70°  C.  could  yield  (30-4-10=)  only  3  calories;  hence  it  could  raise  the 
lk  of  water  only  3°;  i.e.  from  12°  to  15°  C.  Then  it  is  evident  that 
it  must  have  acquired  the  balance  of  (70  —  15=)  55  calories,  by  the 


HEAT  CONVERTIBLE  INTO  POTENTIAL  ENERGY.      145 

restoration  of  the  latent  heat  to  real  heat  when  the  steam  is  liquefied. 
If  the  liquefaction  of  100s  of  steam  yields  55  calories,  then  the  lique^ 
faction  of  lk  of  steam  would  yield  550  calories.  Accurate  methods 
give  537  calories. 

Various  phenomena  show  that  heat  is  developed  during  the  solidifica- 
tion of  liquids,  but  as  the  development  is  slow,  and  the  loss  by  radiation 
rapid,  it  is  difficult  to  make  measurements.  There  are  good  reasons  for 
assuming,  however,  that  there  are  80  calories  of  heat  generated  for  every 
kilogram  of  water  that  is  frozen.  Farmers  sometimes  turn  to  practical 
use  this  well-known  phenomenon.  Anticipating  a  cold  night,  they  carry 
tubs  of  water  into  cellars  to  be  frozen.  The  heat  generated  thereby, 
although  of  a  low  temperature,  is  sufficient  to  protect  vegetables  which 
freeze  at  a  lower  temperature  than  water. 

Steam  is  a  most  convenient  vehicle  for  the  conveyance  of  latent  heat. 
For  example,  every  kilogram  of  steam  that  is  condensed  in  the  radiator 
box  (Fig.  120,  p.  128)  contributes  to  the  air  which  passes  through  the  box 
537  calories,  or  heat  sufficient  to  raise  5.37k  of  ice  water  to  the  boiling- 
point. 

118.  Methods    of   Producing  Artificial  Cold.  —  The 

fact  that  heat  must  be  consumed  because  work  is  done,  in 
the  conversion  of  solids  into  liquids  and  liquids  into 
vapors,  is  turned  to  practical  use  in  many  ways  for  the 
purpose  of  producing  artificial  cold.  The  following  ex- 
periments will  illustrate. 

119.  Cold  by  Dissolving.  —  Freezing  Mixtures. 

Experiment  107.  —  Prepare  a  mixture  of  2  parts,  by  weight,  of 
pulverized  ammonium  nitrate  and  1  part  of  ammonium  chloride. 
Take  about  75CC  of  water  (not  warmer  than  8°  C.),  and  into  it  pour 
a  large  quantity  of  the  mixture,  stirring  the  same,  while  dissolving, 
with  a  test-tube  containing  a  little  cold  water.  The  water  in  the 
test-tube  will  be  quickly  frozen.  A  finger  placed  in  the  solution  will 
feel  a  painful  sensation  of  cold,  and  a  thermometer  will  indicate  a 
temperature. of  about  — 10°  C. 

One  of  the  most  common  freezing  mixtures  consists  of 
3  parts  of  snow  or  broken  ice  and  1  part  of  common  salt. 
The  affinity  of  salt  for  water  causes  a  liquefaction  of  the 


146  MOLECULAR    ENERGY. HEAT. 

ice,  and  the  resulting  liquid  dissolves  the  salt,  both  opera- 
tions requiring  heat. 

12O.     Cold  by  Evaporation. 

Experiment  108.  —  Fill  the  palm  of  the  hand  with  ether;  the 
ether  quickly  evaporates,  and  produces  a  painful  sensation  of  cold. 

Experiment  109.  —  Place  water  at  about  30°  C.  in  a  thin  porous 
cup,  such  as  is  used  in  the  Grove's  battery,  and  the  same  amount  of 
water,  at  the  same  temperature,  in  a  glass  beaker  of  as  nearly  as  pos- 
sible the  same  size  as  the  porous  cup.  Introduce  into  each  a  chemi- 
cal thermometer.  The  comparatively  large  amount  of  surface  exposed 
by  means  of  the  porous  vessel  will  so  hasten  the  evaporation  in  this 
vessel,  that,  in  the  course  of  10  to  15 
minutes,  quite  a  sensible  difference  of 
temperature  will  be  indicated  by  the 
thermometers  in  the  two  vessels. 

Experiment  110.  —  Cover  closely  the 
bulb  of  an  air  thermometer  (Fig.  132) 
with  thin  muslin,  and  partly  fill  the  stem 
with  water.  Let  one  person  slowly  drop 
ether  on  the  bulb,  while  another  briskly 
blows  the  air  charged  with  vapor  away 
from  the  bulb  with  a  bellows ;  or,  place 
the  bulb  in  a  window  whose  sash  is  raised 
a  little  way,  so  as  to  be  in  a  draft.  As 

the  air  changes  rapidly,  it  does  not  become  saturated  with  vapor  so 
as  to  impede  evaporation,  and  in  10  to  15  minutes  the  water  in  the 
stern  freezes,  even  in  a  warm  room. 

The  evaporation  of  perspiration  conduces  to  our  health  and  comfort  by 
relieving  us  of  surplus  heat.  We  cool  the  fevered  forehead  by  bathing  it 
with  a  volatile  liquid,  such  as  a  solution  of  alcohol  in  water.  Windy  days 
seem  colder  to  us  than  still  days,  although  the  temperature  of  both  is  the 
same,  because  evaporation  of  perspiration  takes  place  more  rapidly  in  a 
changing  air.  Fanning  in  a  similar  way  changes  the  air  next  our  persons, 
thereby  quickening  the  evaporation  of  the  perspiration,  and  cooling  the 
surface  of  the  body.  Ice  is  now  manufactured  in  large  quantities  during 
the  summer  season  in  warm  climates  by  the  evaporation  of  liquid  ammo- 
nia. Evaporation  is  the  most  efficient  means  of  producing  extremely 
low  temperatures. 


HEAT  CONVERTIBLE  INTO  POTENTIAL  ENERGY.      147 

QUESTIONS. 

1.  How  can  water  be  made  to  boil  at  a  low  temperature  ? 

2.  Upon  what  does  the  tension  of  steam  depend  ? 
2.  Why  can  you  not  make  ice  warm  ? 

4.  Does  ice  always  have  the  same  temperature ;  i.e.  can  it  be  made 
colder  than  32°  F.  ? 

5.  What  is  the  lowest  temperature  any  body  can  have  ? 

6.  (a)  Where  does  the  "  sweat "  on  ice-pitchers  come  from  ?  (6)  Where 
does  dew  on  grass  come  from  ?    (c)  How  are  clouds  formed  ? 

7.  (a)  When   the   sweat   on   ice-pitchers  is  very  abundant,  what 
does  it  indicate  about  dew-point  ?    (b)  Does  it  forebode  fair  or  rainy 
weather  ? 

8.  How  will  you  easily  show  that  ether  boils  at  a  lower  tempera- 
ture than  water? 

9.  In  which  will  vegetables  cook  quicker,  —  in  fresh  or  salt  water  ? 

10.  How  could  you  separate  the  alcohol  of  rum  or  brandy  from 
the  watery  part  ? 

11.  (a). On  what  kind  of  days  do  clothes  dry  fastest?    (6)  WTill 
frozen  clothes  dry? 

12.  (a)  How  does  heat  dry  the  air  ?    (b)  How  does  heat  dry  clothes  ? 

13.  Suppose   that  10k  of  steam,  at  100°  C.,  is  condensed  in  the 
steam-pipe  in  the  radiator  box,  Figure  120,  per  hour ;  how  much  heat 
will  it  furnish  to  the  surrounding  air  ? 

14.  How  much  heat  will  be  produced  by  freezing  one  cubic  foot 
(about  29k  or  02.5  pounds)  of  water? 

15.  (a)  When   the   barometric   column   stands    at    760mm,  what 
quantity  of  heat  must  be  applied  to  5k  of  icer  at  0°C  to  convert  it 
into  steam  in  an  open  vessel  ?    (7>)  What  will  be  the  temperature  of 
the  steam  at  the  instant  of  generation  ?    (c)  How  much  of  the  heat 
applied  is  rendered  latent  during  the  conversion  from  ice  to  steam  ? 

16.  Is  there  any  reason  why  the  boiling  point  of  water  in  an  open 
vessel  should  be  different  on  the  top  of  a  mountain  from  what  it  is 
at  its  base  ? 

17.  Why  does  ice  melt  slowly  even  in  warm  places? 

18.  10k  of  water  at  100°C  will  melt  how  much  ice  at  0°? 

19.  The  freezing  of  the  water  of  lakes  and  other  bodies  of  water 
tends  to  produce  what  change  in  the  temperature  of  the  air  ? 

20.  Why  does  not  all  the  water  in  a  tea-kettle  flash  into  steam  at 
the  instant  it  reaches  its  boiling  point  ? 


148  MOLECULAR   ENERGY.  —  HEAT. 

Section  VII. 

HEAT   CAPACITY. 

121.  Heat  Capacity,  Specific  Heat.  —  The  expression 
heat  capacity  applied  to  a  body  refers  to  the  quantity  of 
heat  necessary  to  raise  the  temperature  of  the  body  1°. 
The  expression  specific  heat l  is  applied  only  to  some  par- 
ticular substance  and  refers  to  the  quantity  of  heat  required 
to  raise  one  kilogram  of  that  substance  from  4°  to  5°  C. 
It  is  apparent  that  the  specific  heat  of  a  substance  is  the  heat 
capacity  of  1  unit  of  mass  of  that  substance. 

Experiment  111.  — Mix  lk  of  water  at  0°  with  lk  at  20°;  the 
temperature  of  the  mixture  becomes  10°.  The  heat  that  leaves  lk  of 
water  when  it  falls  from  20°  to  10°  is  just  capable  of  raising  lk  of 
water  from  0°  to  10°. 

Experiment  112. — Take  (say)  300  g  of  sheet  lead,  make  a  loose 
roll  of  it,  and  suspend  it  by  a  thread  in  boiling  water  for  about  five 
minutes,  that  it  may  acquire  the  same  temperature  (100°  C.)  as  the 
water.  Remove  the  roll  from  the  hot  water,  and  immerse  it  as 
quickly  as  possible  in  300  g  of  water  at  0°,  and  introduce  the  bulb  of 
a  thermometer  Note  the  temperature  of  the  water  when  it  ceases 
to  rise,  which  will  be  found  to  be  about  3°  (accurately  3.3°  +).  The 
lead  cools  very  much  more  than  the  water  warms.  The  temperature 
of  lead  falls  about  33°  for  every  degree  an  equal  mass  of  water  is 
warmed. 

From  Experiment  111  we  infer  that  a  body  in  cooling  a 
certain  number  of  degrees  gives  to  surrounding  bodies  as 
much  heat  as  it  takes  to  raise  its  temperature  the  same 

1  The  specific  heat  of  a  substance  is  often  defined  as  the  ratio  of  the  heat  capacity 
of  a  body  of  that  substance  to  the  heat  capacity  of  an  equal  mass  of  water. 


HEAT    CAPACITY.  149 

number  of  degrees.  From  Experiment  112  we  learn  that 
the  quantity  of  heat  that  raises  lk  of  lead  from  3.3°  -)-  to 
100°,  when  transferred  to  water,  can  raise  lk  of  water  only 
from  0°  to  3.3°.  Hence  we  conclude  that  equal  quantities 
of  heat,  applied  to  equal  masses  of  different  substances,  raise 
their  temperatures  unequally. 

If  equal  masses  of  mercury,  alcohol,  and  water  receive  equal  quantities 
of  heat,  the  mercury  will  rise  30°,  and  the  alcohol  nearly  2°,  for  every 
degree  the  water  rises.  From  this  we  infer  that  to  raise  equal  masses  of 
each  of  these  substances  1°  requires  30  times  as  much  heat  for  the  water 
as  for  the  mercury,  and  twice  as  much  as  for  the  alcohol.  Since  a  given 
quantity  of  heat  affects  the  temperature  of  a  given  mass  of  water  less 
than  that  of  an  equal  mass  of  mercury  or  alcohol,  water  is  said  to  have 
greater  specific  heat  than  these  substances.  It  is  also  apparent  that  a 
given  mass  of  water  in  cooling  imparts  to  surrounding  bodies  more  heat 
than  the  same  masses  of  mercury  and  alcohol  would  impart  in  cooling  the 
same  number  of  degrees,  in  proportion  to  its  greater  specific  heat. 

"  The  vast  influence  which  the  ocean  must  exert  as  a  moderator  of  cli- 
mate here  suggests  itself.  The  heat  of  summer  is  stored  up  in  the  ocean, 
and  slowly  given  out  during  the  winter.  This  is  one  cause  of  the  absence 
of  extremes  in  an  island  climate." 

j  The  high  specific  heat  of  water  is  utilized  in  heating  buildings  by  hot 
water. 

122.  Method  of  Measuring  Specific  Heat.— A  known  mass 
m  (in  kilograms)  of  the  substance  of  which  the  specific  heat  is  required 
is  taken,  as  in  Experiment  112,  and  heated  to  a  known  temperature  ti 
(C.);  then  it  is  mixed  with  (or  immersed  in)  a  known  mass  of  water  w2  at 
a  lower  temperature  t%,  and  as  soon  as  thermal  equilibrium  is  established 
throughout,  the  temperature  of  the  mixture  t  is  taken.  Let  s  represent  the 
specific  heat  of  the  substance  sought.  Then  the  quantity  of  heat  lost  by  the 
substance  is  m  X  3  (ti  —  t)  calories  ;  while  that  gained  by  the  water  is  mz 
(t  —  £2)  calories.  Now  if  no  heat  be  lost  during  the  operation,  m  X  s 

fa  —  t)  —  mz(t  —  t2)  whence  s  =^-77 ±r'.     For  example,   taking   the 

in  \i>\     f ) 

quantities  obtained  in  Experiment  112,  we  find  for  lead  (300  g==c=.3k) 


150  MOLECULAR    ENERGY.  —  HEAT. 

Section  VIII. 

THERMO-DYNAMICS. 

123.  Therm  o-dynamics  Defined.  —  Thermo-dynamics  is 
that  branch  of  science  that  treats  of  the  relation  between  heat 
and  mechanical  work.     One  of  the  most  important  discov- 
eries in  science  is  that  of  the  equivalence  of  heat  and  work; 
that  is,  that  a  definite  quantity  of  mechanical  work,  when 
transformed  "without  waste,  will  yield  a  definite  quantity  of 
heat;  and  conversely,  this  heat,  if  there  were  no  waste,  could 
perform  the  original  quantity  of  mechanical  work. 

124.  Transformation,  Correlation,  and  Conservation 
of  Energy.  —  The  proof  of  the  facts  just  stated  was  one  of 
the  most  important  steps  in  the  establishment  of  the  grand 
twin  conceptions  of  modern  science  :    (1)  That  all  kinds  of 
energy  are  so  related  to  one  another  that  energy  of  any  kind 
can  be  transformed  into  energy  of  any  other  kind,  —  known 
as  the  doctrine  of  CORRELATION  OF  ENERGY;  (2)  That 
when  one  form  of  energy  disappears,  an  exact  equivalent  of 
another  form  always  takes  its  place,  so  that  the  sum  total  of 
energy  is  unchanged,  —  known  as  the  doctrine  of  CONSER- 
VATION OF  ENERGY.     These  two  principles  constitute  the 
corner-stone  of  physical  science.     Chemistry  teaches  that 
there  is  a  conservation  of  matter. 

125.  Joule's  Experiment.  —  The  experiment  to  ascer- 
tain the  "mechanical  value  of  heat,"  as  performed  by  Dr. 
Joule  of  England,  was  conducted  about  as  follows.     He 
caused  a  paddle-wheel  to  revolve  in  water,  by  means  of  a 
tailing  weight  attached  to  a  cord  wound  around  the  axle 


THERMO-DYNAMICS.  151 

of  a  wheel.  The  resistance  offered  by  the  water  to  the 
motion  of  the  paddles  was  the  means  by  which  the  mechan- 
ical energy  of  the  weight  was  converted  into  heat,  which 
raised  the  temperature  of  the  water.  Taking  a  body  of  a 
known  weight,  e.g.  80k,  he  raised  it  a  measured  distance, 
e.g.  53m  high;  by  so  doing  4,240kgm  of  work  were  performed 
upon  it,  and  consequently  an  equivalent  amount  of  energy 
was  stored  up  in  it  ready  to  be  converted,  first  into  me- 
chanical motion,  then  into  heat.  He  took  a  definite 
weight  of  water  to  be  agitated,  e.g.  2k,  at  a  temperature  of 
0°  C.  After  the  descent  of  the  weight,  the  water  was 
found  to  have  a  temperature  of  5°  C. ;  consequently  the 
2k  of  water  must  have  received  10  units  of  heat  (careful 
allowance  being  made  for  all  losses  of  heat),  which  is  the 
amount  of  heat-energy  that  is  equivalent  to  4,240kgm  of 
work,  or  one  unit  of  heat  is  equivalent  to  424*^m  of  work. 

126.  Mechanical  Equivalent  of  Heat.  —  As  a  con- 
verse of  the  above  it  may  be  demonstrated  by  actual  ex- 
periment that  the  quantity  of  heat  required  to  raise  lk  of 
water  from  4°  to  5°  C.  will,  if  converted  into  work,  raise  a 
424k  weight  lm  high,  or  lk  weight  424m  high.  According 
to  the  English  system,  the  same  fact  is  stated  as  follows : 
The  quantity  of  heat  that  will  raise  1  pound  of  water  1°  F. 
will  raise  772.55  pounds  1  foot  high.  The  quantity,  424kgm, 
is  called  the  mechanical  equivalent  of  one  calorie,  or  Joule's 
equivalent  (abbreviated  simply  J.).  Or,  we  may  say  that 
one  calorie  is  the  thermal  equivalent  of  424kgm  of  work. 


152  MOLECULAR    ENERGY. HEAT. 

Section  IX. 

STEAM-ENGINE. 

127.  Description  of  a  Steam-Engine.  —  A  steam-en- 
gine is  a  machine  in  which  the  elastic  force  of  steam  is  the 
motive  power.  Inasmuch  as  the  elastic  force  of  steam  is 
entirely  due  to  heat,  the  steam-engine  is  properly  a  heat  en- 
gine ;  that  is,  it  is  a  machine  by  means  of  which  heat  is 
continuously  transformed  into  work  or  mechanical  motion. 

The  modern  steam-engine  consists  essentially  of  an  ar- 
rangement by  which  steam  from  a  boiler  is  conducted  to 
both  sides  of  a  piston  alternately ;  and  then,  having  done 
its  work  in  driving  the  piston  to  and  fro,  is  discharged 
from  both  sides  alternately,  either  into  the  air  or  into  a 
condenser.  The  diagram  in  Figure  133  will  serve  to  illus- 
trate the  general  features  and  the  operation  of  a  steam-en- 
gine. The  details  of  the  various  mechanical  contrivances 
are  purposely  omitted,  so  as  to  present  the  engine  as  nearly 
as  possible  in  its  simplicity. 

In  the  diagram,  B  represents  the  boiler,  F  the  furnace, 
S  the  steam-pipe  through  which  steam  passes  from  the 
boiler  to  a  small  chamber  VC,  called  the  valve-chest.  In 
this  chamber  is  a  slide-valve  V,  which,  as  it  is  moved  to 
and  fro,  opens  and  closes  alternately  the  passages  M  and 
N  leading  from  the  valve-chest  to  the  cylinder  C,  and  thus 
admits  the  steam  alternately  each  side  of  the  piston  P. 
When  one  of  these  passages  is  open,  the  other  is  always 
closed.  Though  the  passage  between  the  valve-chest  and 
the  space  in  the  cylinder  on  one  side  of  the  piston  is 
closed,  thereby  preventing  the  entrance  of  steam  into  this 
space,  the  passage  leading  from  the  same  space  is  open 


STEAM-ENGINE. 


153 


through  the  interior  of  the  valve,  so  that  steam  can  escape 
from  this  space  through  the  exhaust-pipe  E.  Thus,  in  the 
position  of  the  valve  represented  in  the  diagram,  the  pas- 
sage N  is  open,  and  steam  entering  the  cylinder  at  the  top 
drives  the  piston  in  the  direction  indicated  by  the  arrow. 
At  the  same  time  the  steam  on  the  other  side  of  the  piston 
escapes  through  the  passage  M  and  the  exhaust-pipe  E. 
While  the  piston  moves  to  the  left,  the  valve  moves  to  the 


Fig.  133. 

right,  and  eventually  closes  the  passage  N  leading  from 
the  valve-chest,  opens  the  passage  M  into  the  same,  and 
thus  the  order  of  things  is  reversed. 

Motion  is  communicated  by  the  piston  through  the 
piston-rod  R  to  the  crank  G,  and  by  this  means  the  shaft 
A  is  rotated.  Connected  with  the  shaft  by  means  of  the 


154          MOLECULAR  ENERGY.  —  HEAT. 

crank  H  is  a  rod  R'  which  connects  with  the  valve  V,  so 
that,  as  the  shaft  rotates,  the  valve  is  made  to  slide  to  and 
fro,  and  always  in  the  opposite  direction  to  that  of  the 
motion  of  the  piston. 

The  shaft  carries  a  fly-wheel  W.  This  is  a  large,  heavy 
wheel,  having  the  larger  portion  of  its  weight  located  near 
its  circumference;  it  serves  as  a  reservoir  of  energy  which 
is  needed  to  make  the  rotation  of  the  shaft  and  all  other 
machinery  connected  with  it  uniform,  so  that  sudden 
changes  of  velocity  resulting  from  sudden  changes  of  the 
driving  power  or  resistances  are  avoided.  By  means  of  a 
belt  passing  over  the  wheel  W  motion  may  be  communi- 
cated from  the  shaft  to  any  machinery  desirable. 

128.  Condensing  and  Non-Condensing  Engines.1  — 
Sometimes  steam,  after  it  has  done  its  work  in  the  cylin- 
der, is  conducted  through  the  exhaust-pipe  to  a  chamber 
Q,  called  a  condenser,  where,  by  means  of  a  spray  of  cold 
water  introduced  through  a  pipe  T,  it  is  suddenly  con- 
densed. This  water  must  be  pumped  out  of  the  condenser 
by  a  special  pump,  called  technically  the  air-pump  ;  thus 
a  partial  vacuum  is  maintained.  Such  an  engine  is  called 
a  condensing  engine.  The  advantage  of  such  an  engine  is 
obvious,  for  if  the  exhaust-pipe,  instead  of  opening  into  a 
condenser,  communicates  with  the  outside  air,  as  in  the 
non-condensing  engine,  the  steam  is  obliged  to  move  the 
piston  constantly  against  a  resistance  arising  from  atmos- 
pheric pressure  of  15  pounds  for  every  square  inch  of  the 
surface  of  the  piston.  But  in  the  condensing  engine  no 
resistance  arises  from  atmospheric  pressure,  and  so  with  a 
given  steam  pressure  in  the  boiler  the  effective  pressure 
on  the  piston  is  considerably  increased ;  hence,  condensing 
engines  are  usually  more  economical  in  their  working. 

1  The  terms,  low-pressure  and  high-pressure  engines,  are  not  distinctive  as  applied  to 
engines  of  the  present  day. 


STEAM-ENGINE. 


155 


129.  Compound  Condensing  Engine.  —  This  engine  has  two 
cylinders,  each  like  that  of  a  simple  engine.  One,  A  (Fig.  134),  called 
the  high-pressure  cylinder,  receives  steam  of  very  high  pressure  directly 
from  the  boiler  through  the  orifice  V.  The  steam,  after  it  has  done  work  in 
this  cylinder,  passes  through  the  steam-port  E  into  cylinder  B,  called  the 
low-pressure  cylinder.  Cylinder  B  is  larger  than  cylinder  A.  The  steam 
which  enters  cylinder  B  possesses  considerable  pressure,  and  is  therefore 
capable  of  doing  considerable  work  under  suitable  conditions.  It  should 
be  borne  in  mind  that  in  order  that  steam  may  do  work  in  any  cylinder,  it 
is  necessary  that  an  inequality  in  the  pressure  of  the  steam  each  side  of  the 


Fig.  134. 

piston  should  be  maintained  ;  just  as  an  inequality  of  level,  i.e.  a  head,  is 
essential  to  water-power.  The  steam,  after  it  has  done  its  work  in  cylin- 
der B,  passes  through  a  port  C  into  a  condenser  (not  represented  in  the 
figure),  where  it  is  suddenly  condensed  or  let  down  to  a  very  low  pressure. 
If  a  vertical  glass  tube  were  led  from  the  condenser  to  a  vessel  of  mercury 
below,  the  mercury  would  ordinarily  stand  about  25  inches  high  in  the 
tube,  which  would  show  that  the  pressure  of  the  steam  against  which  the 
steam  when  it  enters  cylinder  B  does  work,  is  only  about  one-sixth  of  an 
atmosphere.  Much  energy  is  economized  by  the  compound  engine. 

13O.  The  Locomotive.  —  The  distinctive  feature  of  the  locomo- 
tive engine  is  its  great  steam-generating  capacity,  considering  its  size 
and  weight,  which  are  necessarily  limited.  To  do  the  work  ordinarily 
required  of  it,  from  three  to  six  tons  of  water  must  be  converted  into 


156  STEAM-ENGINE. 

steam  per  hour.  This  is  accomplished  in  two  ways :  viz.,  first,  by  a  rapid 
combustion  of  fuel  (from  a  quarter  of  a  ton  to  a  ton  of  coal  per  hour) ; 
second,  by  bringing  the  water  in  contact  with  a  large  extent  (about  800 
square  feet)  of  heated  surface.  The  fire  in  the  "fire-box"  A  (Fig.  135, 
Plate  II.)  is  made  to  burn  briskly  by  means  of  a  powerful  draft 
which  is  created  in  the  following  manner :  The  exhaust  steam,  after  it 
has  done  its  work  in  the  cylinders  B,  is  conducted  by  the  exhaust-pipe  C 
to  the  smoke-box  D,  just  beneath  the  smoke-stack  E.  The  steam,  as  it 
escapes  from  the  blast-pipe  F,  pushes  the  air  above  it,  and  drags  by  fric- 
tion the  air  around  it,  and  thus  produces  a  partial  vacuum  in  the  smoke- 
box.  The  external  pressure  of  the  atmosphere  then  forces  the  air  through 
the  furnace  grate  and  hot-air  tubes  G,  and  thus  causes  a  constant  draft. 
The  large  extent  of  heated  surface  is  secured  as  follows :  The  water  of 
the  boiler  is  brought  not  only  in  contact  with  the  heated  surface  of  the 
fire-box,  but  it  surrounds  the  pipes  G  (a  boiler  usually  contains  about 
150).  These  pipes  are  kept  hot  by  the  heated  gases  and  smoke,  all  of 
which  must  pass  through  them  to  the  smoke-box  and  smoke-stack. 

The  steam-engine,  with  all  its  merits  and  with  all  the 
improvements  which  modern  mechanical  art  has  devised, 
is  an  exceedingly  wasteful  machine.  The  best  engine  that 
has  been  constructed  utilizes  only  about  twenty  per  cent  of 
the  heat-power  generated  by  the  combustion  of  the  fuel. 

QUESTIONS. 

1.  What  kind  of  engine  (i.e.  condensing  or  n  on- condensing)  is  that 
which  produces  loud  puffs?    What  is  the  cause  of  the  puffs? 

2.  Why  does  the  temperature  of  steam  suddenly  fall  as  it  moves 
the  piston  ? 

3.  What  do  you  understand  by  a  ten  horse-power  steam-engine? 

4.  Upon  what  does  the  power  of  a  steam-engine  depend? 

5.  Is  the  compound  engine  a  condensing  or  a  non-condensing  en- 
gine ?    Which  is  the  locomotive  engine  ? 

6.  The  area  of  a  piston  is  500  square  inches,  and  the  average  unbal- 
anced steam  pressure  is  30  pounds  per  square  inch ;  what  is  the  total 
effective  pressure  ?     Suppose  that  the  piston  travels  30  inches  at  each 
stroke,  and  makes  100  strokes  per  minute,  allowing  40  per  cent  for 
wasted  energy,  what  power  does  the  engine  furnish,  estimated  in 
horse-powers  ? 


CHAPTER  VI. 

ELECTRO-STA  TICS. 

Section  I. 

INTRODUCTION. 

131.  Electrification.  —  Certain  bodies,  when  the  con- 
ditions are  suitable,  acquire  by  contact  and  subsequent 
separation  (or  more  readily  by  friction)  the  property  of 
attracting  light  bodies  such  as  pieces  of  tissue  paper,  etc. 
For  example,  glass  rubbed  with  silk,  and  sealing-wax  or 
ebonite    with   woolen    cloth,    manifest   this   property   by 
picking  up  scraps  of  paper,  etc.     Bodies  in  this  state  are 
said  to  be  electrified  or  charged  with  electricity. 

Experiment  113.  —  Rub  a  rubber  comb  with  a  woolen  cloth  or 
draw  it  a  few  times  through  your  hair  (if  dry).  Hold  the  comb 
over  a  handful  of  bits  of  tissue  paper ;  the  papers  quickly  jump  to 
the  comb,  stick  to  it  for  an  instant,  and  then  leap  energetically  from 
it.  The  papers  are  first  attracted  to  the  comb,  but  in  a  short  time 
acquire  some  of  its  electrification,  and  then  are  repelled. 

132.  Two  Kinds  of  Electrification. 

Experiment  114.  —  Suspend  a  ball  of  elder  pith,  C  (Fig.  136),  by 
a  silk  thread.  Electrify  a  glass  rod  D  with  a  silk  handkerchief  and 
present  it  to  the  ball;  attraction  at  first  occurs,  followed  by  repulsion 
soon  after  contact.  Next  excite  a  stick  of  sealing-wax  or  a  rubber 
comb  with  a  woolen  cloth  and  present  it  to  the  ball  which  is 


158 


ELECTRO-STATICS. 


repelled  by  the  electrified  glass  ;  the  ball  is  attracted  by  the  electrified 
wax  or  rubber. 


It   is   evident    (1) 


Fig.  136. 


that  there  are  two  kinds  or  •  condi- 
tions of  electrification  ;  (2) 
that  bodies  similarly  elec- 
trified repel  one  another, 
bodies  oppositely  electri- 
fied attract  one  another. 

Glass  rubbed  with  silk 
is  said  to  receive  a  charge 
of  vitreous  electrification ; 
the  wax,  after  being 
rubbed  with  woolen 
cloth,  on  the  other  hand,  is  charged  with  resinous 
electrification.  Vitreous  charges  are  said  to  be  positive 
(written  +E),  and  resinous  negative  (written  — E). 

Experiment  115.  —  Once  more  electrify  a  stick  of  sealing-wax 
with  a  woolen  cloth,  and  present  it  to  the  pith  ball,  and  after  the  ball 
is  repelled,  bring  the  surface  of  the  flannel  which  had  electrified  the 
rod  near  the  ball;  the  ball  is  attracted  by  it,  showing  that  the  rubber 
is  also  electrified,  and  with  the  opposite  kind  to  that  which  the 
sealing-wax  possesses. 

One  kind  of  electrification  is  never  developed  alone  ; 
when  two  substances  are  rubbed  together,  and  one  becomes 
electrified,  electrification  of  the  opposite  kind  is  always 
developed  in  the  other. 

133.    Electrification  a  Form  of  Potential  Energy.  - 

When  small  pieces  of  glass  and  silk  are  rubbed  together, 
it  is  found  that  after  they  are  pulled  apart  they  attract 
each  other  with  a  definite  and  measurable  force  ;  and  that 
this  force  varies  inversely  as  the  square  of  the  distance 


INTRODUCTION. 


159 


between  them.  When  two  bodies  are  pulled  apart,  energy 
is  expended  upon  them  which  will  be  restored  when  they 
are  allowed  to  approach  each  other.  It  is  certain  that 
electrification  is  the  result  of  work  done,  and  is  a  form  of 
potential  energy. 

134.  What  is  Electricity  ?  —  The  student  naturally 
has  already  begun  to  ask  the    never-answered  question, 
"What  is  electricity?"  and  to  inquire,    "  What  is  the 
function  of  electricity  in  these  operations  ?  "     Provision- 
ally we  shall  regard  electricity  as  that  which  is  transferred 
from  one  body  to  another  body  when  the  two  become 
oppositely  electrified.     Electricity  is  not  a  form  of  energy. 
It  is  quite  true  that  electricity  under  pressure  or  in  motion 
possesses  energy  ;    in  the  same  sense   do  water  and  air 
under  like  conditions  possess  energy,  but  no  one  presumes 
to  call  them  forms  of  energy. 

135.  Electroscope.  —  This   is  an  instrument  used  to 
detect  the  presence  of  electrification  in  a  body,  and  to 
determine  its  kind.     It  usu- 
ally consists  of  two  strips  of 

gold  foil,  A  B  (Fig.  137), 
suspended  from  a  brass  rod 
within  a  glass  jar.  To  the 
upper  end  of  the  rod  is  fixed 
a  metal  disk,  C.  On  the 
opposite  sides  of  the  interior 
of  the  jar  are  two  strips  of 
metal  foil,  D  and  E,  of  suf- 
ficient hight  to  be  touched 
by  the  strips  A  and  B  on 
their  extreme  divergence.  Fig.  137. 


160  ELECTRO-STATICS. 

(1)  If    an    unelectrified    body   be    brought   near   the 
disk  C,  no  change  takes  place  in  the  two  strips  of  foil  A 
and  B,  but  if  an  electrified  body  be  brought  near  the  disk, 
the  strips  diverge,  thus   indicating   the    existence    of   a 
charge  of  electricity  in  the  body. 

(2)  If  the  electroscope  be  charged  by  contact  with  an 
excited  body,  the  strips  will  remain  in  a  divergent  posi- 
tion.   While  they  are  in  this  condition,  if  a  body  similarly 
charged  be  brought  near  the  disk,  the  strips  will  diverge 
more;    but  if  an  unexcited  body  or  a   body  oppositely 
electrified  be  brought  near  the  disk,  the  strips  will  collapse. 

136.    Conduction. 

Experiment  116.  —  a.  Rub  a  brass  tube,  held  in  the  hand,  with 
warm  silk.  Bring  it  near  the  disk  of  the  electroscope  ;  the  leaves 
are  unaffected,  b.  Wrap  a  piece  of  sheet  rubber  around  one  end  of 
the  tube  and  hold  this  end  in  the  hand,  and  rub  as  before.  Bring  it 
near  the  disk  of  the  electroscope  ;  notice  that  the  leaves  diverge. 
c.  Repeat  the  last  operation  ;  but  before  bringing  the  tube  near  the 
disk  touch  the  tube  with  a  finger.  The  leaves  no  longer  show  signs 
of  electrification. 

In  the  first  (a)  and  last  (c)  operations  electricity  escaped 
through  the  hand  and  body  to  the  earth  ;  in  the  second  (b) 
it  was  prevented  from  escaping  by  the  intervening  sheet 
rubber.  Substances  which  allow  electricity  to  spread  over 
them,  i.e.  substances  which  offer  little  resistance  to  the 
flow  of  electricity,  are  called  conductors.  Those  which 
offer  great  resistance  to  its  passage  are  called  non-con- 
ductors, insulators,  or  dielectrics. 

Some  of  the  best  insulating  substances  are  dry  air, 
ebonite,  shellac,  resins,  glass,  silks,  and  furs.  On  the  other 
hand,  metals  are  exceedingly  good  conductors.  Moisture 


INDUCTION.  161 

injures  the  insulation  of  bodies  ;  hence  experiments  suc- 
ceed best  on  dry,  cold  days  of  winter,  when  moisture  of 
the  air  is  least  liable  to  be  condensed  on  the  surfaces  of 
apparatus,  especially  if  the  latter  be  kept  warm. 

Water  cannot  be  retained  in  a  reservoir  unless  its  walls 
be  of  sufficient  strength  ;  so  a  body,  in  order  to  become 
charged  and  to  retain  the  charge,  must  be  surrounded  by 
something  that  will  offer  sufficient  resistance  to  the  escape 
of  electricity.  There  is  no  limit  to  the  quantity  of  electri- 
city with  which  a  body  can  be  charged,  provided  the 
charge  can  be  retained.  This  entity  which  represents  the 
walls  of  the  reservoir  is  termed  the  dielectric.  It  may  be 
the  air  or  any  of  the  so-called  non-conductors  of  electricity. 
A  body  thus  surrounded  is  said  to  be  insulated. 


Section  II. 

INDUCTION. 

137.    Electricity  acts  across  a  Dielectric. 

Experiment  117.  —  Figure  138  represents  an  empty  egg-shell  cov- 
ered with  tin  foil  to  make  it  a  good  conductor.  It  is  suspended  from 
a  glass  rod  by  a  silk  thread,  a.  Electrify  a  glass  rod  and  bring 
it  near  the  shell.  The  shell  moves  toward  the  rod.  b.  Next 
introduce  a  glass  plate  between  the  rod  and  shell.  The  shell  ap- 
proaches the  rod  as  before. 

The  chief  lesson  we  learn  from  this  experiment  is  that 
electricity  acts  across  a  dielectric.  In  a  the  dielectric  was 
air  ;  in  6,  air  and  glass. 


162 


ELECTRO-STATICS. 


138.  To  determine  what  actually  happens  on  an 
Insulated  Conductor  when  an  Electrified  Body  is 
brought  near. 

Experiment  118.  —  a.  Suspend,  as  above,  two  shells  so  as  to 

touch  each  other,  end  to  end,  as 
in  Figure  139,  thus  making  prac- 
tically one  conductor.  Bring 
near  to  one  end  of  the  shells  a 
sealing-wax  rod,  D,  excited  with 
— E.  While  the  rod  is  in  this 
position  carry  a  thin  strip  of  tis- 
sue paper,  C,  along  the  shells. 
The-  paper  is  attracted  to  the 
shells,  but  most  strongly  at  the 
ends.  In  the  middle  of  the  con- 
ductor, where  the  shells  touch 
each  other,  there  is  little  if  any 
electrification. 

b.  While  the  rod  D  is  still  in 
position,    separate    B    from    A, 
then  remove  D.     Test  each  shell 
with  the  tissue  paper  ;  both  are  found  to  be  excited. 

c.  Charge  an  electroscope  with  +  E.      Then  bring  A  near  it ;  the 
leaves  diverge,  showing  that  A  is  charged  with  +E.      Bring  B  near 
the  electroscope  ;  the  leaves  collapse,  showing  that  B  is  charged  with 
-E. 

d.  Finally  bring  the  two  shells  near  each  other ;  they  attract  each 
other.     Allow  them  to  touch  each  other,  and  then  test  each  with  the 
tissue  paper  or  the  electroscope  ;    it  will  be  found  that  both  have 
become  discharged. 

From  the  above  operations  we  learn  that  when  an  electri- 
fied body  is  brought  near  but  not  in  contact  with  an  insu- 
lated conductor,  the  electrified  body  acts  across  the  dielec- 
tric upon  the  conductor,  repelling  electricity  of  the  same 


Fig.  138. 


INDUCTION. 


163 


kind  to  the  remote  side  of  the  conductor,  and  attracting 
the  opposite  kind  to  the  side  near  to  it.  Such  electrical 
action  is  called  induction.  The  electrified  body  which 


Fig.    139. 

produces  the  action  is  called  the  inducing  body ;  the 
charge  of  electricity  thus  produced  is  called  induced 
electricity. 

139.    Charging1  by  Induction. 

Experiment  119.  —  Take  a  proof  plane  E  (Fig.  140)  (which 
consists  of  an  insulating  handle  of  glass  or  gutta-percha,  terminating 
at  one  end  with  a  thin  metal  disk,  F,  about  the  size  of  a  5-cent  nickel), 
and  connect  it  with  an  electroscope,  G,  by  a  fine  wire,  H.  Bring  a 
stick  of  sealing-wax  electrified  as  before  with  —  E  near  the  egg-shell 
conductor.  Holding  the  proof  plane  by  the  insulating  handle,  bring 
the  disk  near  the  end  of  the  conductor  charged  by  induction  with 
— E.  The  —  E  will  act  inductively  upon  the  continuous  conductor 
consisting  of  disk,  wire,  and  electroscope,  charging  the  end  nearest 
itself  (i.e.  the  disk)  with  +E  and  the  remote  end  (i.e.  the  leaves) 
with  —  E.  The  leaves  of  the  electroscope  show  the  presence  of  a 
charge  by  their  divergence. 

Now  while  everything  is  in  the  position  indicated  by  the  cut, 
touch  with  the  finger  any  part  of  the  continuous  conductor  ;  the 


164  ELECTRO-STATICS. 

leaves  of  the  elec- 
troscope instantly 
collapse.  The  —  E 
with  which  the 
leaves  had  been 
charged  being/ree  is 
discharged  through 
your  body.  But  the 
+  E  concentrated 
on  the  disk  of  the 
Fig.  14O.  proof  plane  is  bound 

by  the  attraction  of 

the  charge  of  —  E  on  the  end  of  the  shell  nearest  it,  and  cannot  escape. 

Remove  the  finger  from  the  electroscope  and  the  proof  plane  from 

the  influence  of  the  shell ;  the  leaves  again  diverge. 

The  last  phenomenon  is  explained  as  follows  :  After 
—  E  had  been  discharged  from  the  continuous  conductor, 
there  was  left  an  excess  of  -)-  E  ;  but  this  excess  was  all 
concentrated  in  the  disk  F  so  long  as  it  remained  near 
the  negative  charge  of  the  shell.  But  as  soon  as  F  was 
removed  from  the  influence  of  the  shell,  the  charge  spread 
itself  over  the  entire  conductor,  and  the  leaves,  which 
received  a  portion  of  the  charge,  diverged.  The  conductor 
is  said  to  be  charged  by  induction. 

Experiment  120.  —  To  electrify  the  shell  by  induction,  bring  the 
excited  wax  near  it,  touch  the  shell  with  a  finger,  remove  the  finger, 
and  finally  remove  the  rod.  The  proof  plane  being  connected  with 
the  electroscope  and  being  charged  with  —  E,  bring  F  near  to  the 
shell  A  ;  the  leaves  collapse,  showing  that  the  shell  is  charged  with 
+  E,  which  draws  the  —  E  away  from  the  leaves. 

Observe  that  when  a  body  becomes  charged  by  induc- 
tion the  charge  which  it  receives  is  opposite  in  kind  to  that 
of  the  inducing  body. 


ELECTEICAL  POTENTIAL. 


165 


140.  Charging-  by  Conduction. 

Experiment  121.  —  Disconnect  the  proof  plane  from  the  electro- 
scope. Charge  the  electroscope  with  —  E  and  the  shell  with  +E  ; 
touch  the  shell  with  the  disk  of  the  proof  plane,  then  hold  the  disk 
near  the  electroscope  ;  the  divergent  leaves  collapse,  showing  that 
the  disk  bears  +E  which  it  received  by  conduction  from  the  shell 
when  they  were  brought  in  contact.  Of  course  the  charge  is  the 
same  kind  as  that  of  the  body  which  communicated  it. 

141.  Induction  precedes  Attraction.  —  When 
ball  is  brought  near  an  electrified  glass  rod,  the 
the  rod  A  (Fig.  141)  induces  — E  on  the 

side  of  the  ball  B  nearest  A  and  repels 
-j-  E  to  the  farther  side.  The  -f-  E  of  A  and 
the  —  E  of  B  therefore  attract  each  other  ; 
likewise  the  +  E  of  A  and  the  +  E  of  B 
repel  each  other :  but  since  the  former 
charges  are  nearer  each  other  than  the  latter 
are,  the  attraction  exceeds  the  repulsion. 


FIg-  141 


Section  III. 

ELECTRICAL   POTENTIAL. 

142.  Electro-statics  and  Electro-kinetics. — Electric- 
ity may  be  at  rest,  as  in  a  charged  body,  or  it  may  be  in 
motion,  as  in  the  case  of  a  charged  body  connected  by  a 
conductor  with  the  earth,  when  it  is  discharged  through 
the  conductor  to  the  earth.  It  will  be  shown  later  on 
that  as  long  as  a  flow  of  electricity  continues,  the  con- 
ductor along  which  it  flows  has  properties  different  from 


166  ELECTRO-STATICS. 

those  of  a  simple  electrified  body.  That  branch  of  electri- 
cal science  which  treats  of  the  properties  of  simple 
electrified  bodies  is  called  Electro-statics,  because  in  them 
electricity  is  supposed  to  be  at  rest;  and  that  branch 
which  treats  of  electricity  in  motion  is  called  Electro- 
kinetics. 

143.  Potential.  —  The  fundamental  fact  of  electricity 
is  that  we  are  able  to  place  bodies  in  different  electrical 
conditions.  A  charge  of  electricity,  which  implies  an 
abnormal  electrical  condition,  is  the  foundation  of  all 
electrical  phenomena.  We  are  now  to  discuss  the  mean- 
ing and  use  of  the  very  important  term  potential,  with 
reference  to  electricity. 

a.  When  a  charged  conductor  is  connected  with  the 
earth,  a  transfer  of  electricity  takes  place  between  the 
body  and  the  earth. 

b.  If  the  body  be  charged  with  -{-  E,  we  say  arbitrarily 
that  electricity  passes  to  the  earth  ;  but  if  the  body  be 
charged  with  —  E,   electricity  passes  from  the  earth  to 
the  body. 

c.  If  two  insulated  charged  conductors  be  connected 
with  each  other,  electricity  may  or  may  not  pass  from  one 
to  the  other.     Now  whether  electricity  passes  from  one  to 
the  other,  and  in  what  direction  it  passes,  if  at  all,  depends 
upon  the  so-called  potentials  of  the  conductors. 

d.  If  two  bodies  have  the  same  potential,  no  transfer  of 
electricity  takes  place  between  them  when  they  are  con- 
nected by  a  conductor ;  but  if  the  two  bodies  have  different 
potentials,   there  will  be  a  transfer,  and  the  body  from 
which  the  electricity  flows  is  said  to  be  at  a  higher  poten- 
tial than  the  one  to  which  it  flows. 


ELECTRICAL   POTENTIAL.  167 

144.  Definition    of   Potential.  —  The  potential   of  a 
conductor  may,  therefore,  be  defined  provisionally  as  the 
electrical  condition  of  that  conductor  which  determines 
the  direction  of  the  transfer  of  electricity. 

The  term  potential  is  relative.  It  is  important  to  have 
a  standard  of  reference  whose  potential  is  considered  to 
be  zero,  just  as  it  is  convenient  in  stating  the  elevations 
or  depressions  of  the  earth's  surface  to  give  the  distances 
above  or  below  sea-level,  which  is  taken  as  the  zero  of 
hight.  For  experimental  purposes  the  earth  is  usually 
assumed  to  be  at  zero  potential.  A  body  charged  with 
-J-  E  is  understood  to  be  one  that  has  a  higher  potential 
than  that  of  the  earth,  and  a  body  charged  with  —  E  is 
one  that  has  a  lower  potential  than  that  of  the  earth. 

145.  Analogies.  —  Potential    is    analogous,    in   many 
respects,  to  (1)  temperature,  and  to  (2)  liquid  level. 

(1)  When  we  say  that  the  temperature  of  air  is  20°  or 
— 10°  C.,  we  mean  that  its  temperature  is  20°  above  or 
10°  below  the  standard  temperature  of  reference,  viz.  that 
of  melting  ice.     If  two  bodies  at  different  temperatures 
be  placed  in  thermal  communication,  heat  will  pass  from 
the  body  at  a  higher  temperature  to  the  one  at  a  lower, 
and  will  continue  to  do  so  until  both  are  at  the  same 
temperature. 

(2)  If  two  vessels  containing  water  at  different  levels 
be  put  in  communication  at  their  bottoms  by  a  pipe,  water 
will  flow  from  the  one  at  a  higher  level  to  the  one  at  a 
lower   until    the    water   is    at    the    same    level    in    both 
vessels. 

Temperature  is  not  heat ;  level  is  not  water ;  and 
potential  is  not  electricity,  but  merely  the  state  of  the 


168  ELECTRO-STATICS. 

conductor  which  determines  the  direction  of  transfer  of 
electricity. 


Section  IV. 

ATMOSPHERIC   ELECTRICITY. 

146.  Lightning1.  —  Franklin,  by  his  historic  series  of 
experiments,  proved  the  exact  similarity  of  lightning  and 
thunder  to  the  light  and  crackling  of  the  electric  spark. 
Certain  clouds  which  have  formed  very  rapidly  are  highly 
charged,  usually  with  +E,  but  sometimes  with  — E. 
The  surface  of  the  earth  and  objects  thereon  immediately 
beneath  the  cloud  are,  of  course,  charged  inductively 
with  the  opposite  kind  of  electricity.  The  opposite 
charges  on  the  earth  and  on  the  cloud  hold  each  other 
prisoners  by  their  mutual  attraction,  the  air  serving  as  an 
intervening  dielectric. 

As  condensation  progresses  in  the  cloud  its  potential 
rises  (or  sinks).  This  process  continues  till  the  difference 
of  potential  between  the  cloud  and  the  earth  becomes 
great  enough  to  produce  a  discharge  through  the  air. 

It  is  the  accumulation  of  induced  charges  on  elevated 
objects,  such  as  buildings,  trees,  etc.,  that  offers  an 
intensified  attraction  for  the  'opposite  electricity  of  the 
cloud  in  consequence  of  their  greater  proximity,  and 
renders  them  especially  liable  to  be  struck  by  lightning. 

The  clouds  gather  electricity  from  the  atmosphere. 
Our  knowledge  of  the  method  by  which  the  atmosphere 
becomes  charged  is  very  limited. 


169 


CHAPTER  VII. 
ENERGY  OF  ELECTRIC  FLOW.     ELECTRO-KINETICS. 

Section  I. 

VOLTAIC   CELLS.      ELECTRIC   CIRCUITS. 

147.    Introductory  Experiments. 

APPARATUS  REQUIRED.  —  A  tumbler  $•  full  of  water,  into  which  have 
been  poured  two  or  three  tablespoonfuls  of  strong  sulphuric  acid  ;  a  strip 
of  sheet-copper,  and  two  pieces  of  rolled  zinc,  each  about  5  inches  long, 
1£  inches  wide,  and  at  least  T\  of  an  inch  thick  (a  piece  of  No.  16  copper 
wire  12  inches  long  should  be  soldered  to  one  end  of  each  piece  of  metal, 
and  the  soldering  covered  with  asphaltum  paint) ;  2  yds.  of  silk  insulated 
No.  18  copper  wire  ;  two  double 
connectors  (Fig.  142),  which  serve 
to  join  two  wires  without  the  incon- 
venience of  twisting  them  together. 
One  of  the  zincs  should  be  amal- 
gamated as  follows  :.  First  dip  the  zinc,  with  the  exception  of  £  inch  at 
the  soldered  end,  into  the  acidulated  water  ;  then  pour  mercury  over  the 
wet  surface,  and  finally  rub  the  surface,  now  wet  with  mercury,  with  a 
cloth.  (To  insure  complete  amalgamation,  it  is  best  to  repeat  this 
operation.) 

Experiment  122.  —  a.  Put  the  unamalgamated  zinc  into  the  tum- 
bler containing  acidulated  water.  Bubbles  of  hydrogen  gas  arise 
from  the  surface  of  the  immersed  zinc. 

6.  Remove  this  zinc  and  introduce  the  amalgamated  zinc.  No 
bubbles  (or  at  least  very  few)  arise  from  the  latter,  provided  that  the 
zinc  is  properly  amalgamated. 

If  a  plate  of  metal  be  placed  in  a  liquid  of  a  class  which 
we  shall  term  an  electrolyte  (i.e.  one  which  is  capable  of 


170          ENERGY  OF  ELECTRIC  FLOW. 

being  decomposed  by  a  current  of  electricity),  there  is  a 
difference  of  electrical  condition  produced  between  them 
so  that  the  metal  becomes  either  of  higher  or  lower  poten- 
tial than  the  liquid,  according  to  the  nature  of  the  metal 
and  liquid. 

We  know  that  if  two  conductors  be  at  different  poten- 
tials, electricity  tends  to  flow  from  the  one  whose  potential 
is  higher  to  that  whose  potential  is  lower ;  if,  therefore, 
two  dissimilar  metals  be  placed  in  the  same  electrolytic 
liquid,  it  may  be  shown,  by  actual  experiment,1  that  the 
free  end  of  the  wire  in  connection  with  one  plate  is  charged 
with  -f-  E,  and  the  free  end  of  the  other  with  —  E.  Hence 
we  conclude  that  if  the  two  oppositely  charged  bodies  be 
brought  in  contact,  a  current  of  electricity  will  flow  from 
the  positively  charged  plate  to  the  negatively  charged  one. 
A  current  therefore  flows  through  the  connecting  wire 
from  the  copper  (which  is  called  the  positive  electrode)  to 
the  wire  leading  from  the  zinc  (which  is  called  the  nega- 
tive electrode),  when  they  are  connected. 

That  difference  in  quality  in  virtue  of  which  zinc  and 
copper  placed  in  acidulated  water  can  give  rise  to  an  elec- 
trit  current,  is  called  their  electro-chemical  difference,  and 
the  zinc  is  said  to  be  electro-positive  to  the  copper  in  the 
liquid. 

148.  Voltaic  Cell.  —  Two  electro-chemically  different 
solids  (of  which  zinc  is  almost  invariably  one)  placed  in 
an  electrolytic  liquid  constitute  what  is  called  a  galvanic 
or  voltaic2  cell  (or  pair).  One  of  these  plates  must  be 
more  actively  attacked  by  the  liquid  than  the  other ;  the 

1  See  author's  Principles  of  Physics,  p.  463. 

2  A  single  voltaic  couple  is  usually  termed  a  cell ;  a  combination  of  cells,  a  battery. 


VOLTAIC    CELLS.       ELECTRIC    CIRCUITS.  171 

plate  most  acted  upon  is  called  the  electro-positive  plate, 
and  the  other  the  electro-negative  one. 

The  greater  the  disparity  between  the  two  solid  elements 
with  reference  to  the  action  of  the  liquid  on  them,  the  greater 
the  difference  in  potential ;  hence,  the  greater  the  current. 

In  the  following  electro-chemical  series  the  substances  are  so  arranged 
that  the  most  electro-positive,  or  those  most  affected  by  dilute  sulphuric 
acid,  are  at  the  beginning,  while  those  most  electro-negative,  or  those 
least  affected  by  the  acid,  are  at  the  end.  The  arrow  indicates  the 
direction  of  the  current  through  the  liquid. 

I 

fe  &      8 

«      ^      a      o 

i    6       a         •      *x       8*      P      2      •" 

+1   f   a   f  >§•  I  1    s~ 

N£HH;O£PHU 


It  will  be  seen  that  zinc  and  platinum  are  the  two  substances  best 
adapted  to  give  a  strong  current. 

When  the  wires  from  the  two  plates  are  joined,  the  dis- 
charge of  the  two  plates  would  produce  electrical  equilib- 
rium were  there  not  some  means  of  maintaining  a  difference 
of  potential  between  the  two  plates.  This  is  accomplished 
by  the  chemical  action  be  ween  the  liquid  and  the  electro- 
positive plate  and  at  the  expense  of  the  chemical  potential 
energy  of  the  electrolyte  and  plate.  A  voltaic  cell  is,  there- 
fore, a  contrivance  which  converts  chemical  energy  into 
electrical  energy. 

149.  Circuit.  — This  term  is  applied  to  the  entire  path 
along  which  electricity  flows,  and  it  comprises  the  battery 
itself  and  the  wire  or  other  conductor  connecting  the  bat- 
tery-plates.1 Bringing  the  two  extremities  of  the  wire  in 

1  It  was  an  early  discovery  in  telegraphic  history  that  a  complete  metallic  circuit 
is  not  necessary,  but  that,  in  common  parlance,  the  earth  can  be  used  as  a  "  return 
circuit."  This  type  of  circuit  is  represented  by  a  battery  with  a  wire  leading  from 


172  ENERGY  OF  ELECTRIC  FLOW. 

contact  and  separating  them  are  called,  respectively,  clos- 
ing and  opening,  QT  making  and  breaking,  the  circuit.  Open- 
ing a  circuit  at  any  point  and  filling  in  the  gap  with  an 
instrument  of  any  kind  so  that  the  current  is  obliged  to 
traverse  it,  is  called  introducing  the  instrument  into  the 
circuit. 

150.  Importance  of  Amalgamating-  the  Zinc.  —  Com- 
mercial zinc  contains  impurities,  such  as  carbon,  iron,  etc.     Figure  143 

represents  a  zinc  element  having  on  its  surface  a  particle  of 

B^^^s.      carbon  a,  purposely  magnified.    If  such  a  plate  be  immersed 

in  dilute  sulphuric  acid,  the  particles  of  carbon  will  form 

HlS    with  the  zinc  numerous  voltaic  circuits,  and  a  transfer  of 

W oj    electricity  along  the  surface  will  take  place.     This  transfer 

^•fp    between  the  zinc  and  the  impurities  on  its  surface  diverts  so 

much  from  the  regular  battery  current,  and  thereby  weakens 

it.     In  addition  to  this,  it  occasions  a  great  waste  of  mate- 

•  1     rials,  because,  when  the  regular  circuit  is  broken,  this  local 

action,  as  it  is  called,  still  continues.     If  mercury  be  rubbed 

over  the  surface  of  the  zinc  it  dissolves  a  portion  of  the  zinc, 

forming  with  it  a  semi-liquid  amalgam,  which  covers  up  its 

impurities. 

151.  Polarization  of  the  Negative  Element. 

Experiment  123.  —  Construct  a  voltaic  cell  composed  of  dilute 
sulphuric  acid  and  plates  of  copper  and  zinc.  Introduce  into  the 
circuit  a  galvanoscope  (§  159)  and  note  the  deflection  of  the  needle 
when  the  circuit  is  first  closed.  Watch  the  needle  for  a  time.  Little 
by  little  this  deflection  will  decrease,  and  as  it  decreases  bubbles  of 
gas  collect  on  the  copper  plate.  This  accumulation  of  gas  is  called 
"  polarization  of  the  negative  element  or  plate." 

We  already  understand  that  difference  of  potential  is 
indispensable  to  a  flow  of  electricity.  Accompanying  a 
difference  of  potential  there  seems  to  be  something  anal- 
one  plate  to  any  convenient  point  of  the  earth,  and  a  second  wire  leading  from  the 
other  plate  to  any  other  point  of  the  earth,  which  may  he  many  miles  distant  from 
the  first  point. 


VOLTAIC    CELLS.       ELECTRIC    CIRCUITS. 


173 


ogous  to  a  force  which  causes  the  flow  of  electricity 
through  the  circuit.  The  film  of  gas  on  the  copper 
reduces  the  electro-chemical  difference  between  it  and 
the  zinc  plate,  upon  which  the  generation  of  this  force 
depends,  and  thereby  diminishes  the  efficiency  of  the 
battery. 

The  remedy  for  this  is  to  prevent  the  deposit  of  hydro- 
gen upon  the  negative  plate.  The  usual  method  is  to 
employ  in .  addition  to  the  dilute  sulphuric  acid  (i.e.  the 
exciting  liquid)  some  oxidizing  substance  which  will  com- 
bine with  the  hydrogen  as  soon  as  it  is  liberated.  A  sub- 
stance used  for  this  purpose  is  termed  a  depolarizer.  A 
mixture  of  a  solution  of  crystals  of 
bichromate  of  potassium  in  water 
with  a  suitable  quantity  of  dilute 
sulphuric  acid  is  used  as  a  depo- 
larizer in  the  so-called  bichromate 
batteries. 


152.  Grenet  Cell.  —  This  is  a  bi- 
chromate of  potassium  battery  in  which 
two  carbon  plates,  CC  (Fig.  144),  elec- 
trically connected,  and  a  zinc  plate,  Z, 
suspended  between  them  by  a  brass  rod, 
a,  are  immersed  in  the  mixed  liquid  re- 
ferred to  above. 

This  combination  furnishes  a  much 
more  energetic  and  constant  current  than 
would  be  furnished  if  only  dilute  sulphuric 
acid  were  used. 


Fig.  144. 


153.  Bunsen  Cell.  —  A  plan  generally  adopted  to  keep  the  oxi- 
dizing liquid  away  from  the  zinc  plate,  where  it  is  not  wanted  and  only 
does  harm,  is  to  place  the  carbon  plate  in  an  unglazed,  porous,  earthen 
cup  and  to  surround  it  with  the  oxidizing  substance.  This  arrangement, 
called  a  two-fluid  cell,  is  that  adopted  by  Bunsen  (Fig.  145)  and  others. 


174 


ENERGY  OF  ELECTRIC  FLOW. 


154,  Ijeclanch^  Cell.  —  There  is  a  class  of  galvanic  cells  in  which 
the  negative  element  is  protected  from  polarization  by  means  of  metallic 
oxides.  Of  these  the  best  known  is  the  Leclanche"  cell  (Fig.  146).  In 
this  cell  the  carbon  plate  C  is  contained  in  a  porous  cup  P,  and  packed 
round  with  fragments  of  gas-retort  coke  and  manganese  peroxide.  The 
manganese  compound  has  a  strong  affinity  for  the  hydrogen.  But  the 


Fig.  145. 


Fig.  146. 


chemical  action  of  solids  is  sluggish  and  they  quickly  polarize  when  in 
action.  They  need  periodical  rest  to  recover  their  normal  condition. 
Such  are  called  open-circuit  batteries,  since  they  are  suited  for  work  only 
on  lines  kept  open  or  disconnected  most  of  the  time,  such  as  in  telephone 
and  bell-ringing  circuits.  The  zinc  rod  Z  is  immersed  in  a  solution  of 
ammonium  chloride,  which  is  the  exciting  liquid. 


EFFECTS  PRODUCIBLE  BY  AN  ELECTRIC  CURRENT.    175 


Section  II. 

EFFECTS  PRODUCIBLE  BY  AN  ELECTRIC  CURRENT. 

155.  Summary  of  Effects.  —  The  several  effects  pro- 
ducible by  an  electric   current  may  be   classified  as   (1) 
electrolytic,  (2)  magnetic,  (3)  thermal,  and  (4)  physiological. 

156.  (1)   Electrolysis. 


Experiment  124.  —  Take  a  dilute 
solution  of  sulphuric  acid  (1  part  by 
volume  to  20),  pour  some  of  it  into  the 
funnel  (Fig.  147),  so  as  to  fill  the 
U-shaped  tube  when  the  stoppers  are 
removed.  Place  the  stoppers  which 
support  the  platinum  electrodes  tightly 
in  the  tubes.  Connect  with  these 
electrodes  the  battery  l  wires.  Instantly 
bubbles  of  gas  arise  from  both  elec- 
trodes, accumulating  in  the  upper  part 
of  the  tube  and  forcing  the  liquid  back 
into  the  tunnel.  Introduce  a  glowing 
splinter  into  the  gas  surrounding  the 
+  electrode  ;  it  relights  and  burns  vigor- 
ously, showing  that  the  gas  is  oxygen. 
Invert  the  tube,  allow  the  gas  which 
had  accumulated  about  the  —  electrode 
to  escape  at  a,  and  apply  a  lighted  match 
to  it :  the  gas  burns ;  it  is  hydrogen. 


Fig.  147. 


The  volume   of  hydrogen  is  just  double   that  of  the 
oxygen  liberated  in  the  same  time.     The  process  by  which 


l  A  battery  consisting  of  not  less  than  two  Grenet  or  Bunsen  cells  connected  ii 
series  will  be  required. 


176  ENERGY  OF  ELECTRIC  FLOW. 

a  compound  substance  is  separated  into  its  constituents 
is  called  electrolysis,  and  the  compound  thus  treated  is 
called  the  electrolyte.  The  electrode  by  which  the  current 
enters  the  electrolyte  is  called  the  anode;  and  that  by 
which  the  current  leaves,  the  cathode. 

When  a  chemical  salt  is  electrolyzed,  the  base  appears 
at  the  cathode,  and  the  acid  at  the  anode.  In  general  it 
will  be  found  that  in  both  the  battery  and  the  decompos- 
ing cell,  hydrogen,  bases,  and  metals  appear  at  the  plates 
toward  which  the  current  flows. 

Experiment  125.  —  Dissolve  about  three  grains  of  pulverized 
potassium  iodide  in  a  teaspoonful  of  water.  Make  a  paste  by 
boiling  pulverized  starch  in  water.  Take  a  portion  of  this  paste 

about  the  size  of  a  pea,  and 
stir  it  into  the  solution.  Wet  a 
piece  of  writing-paper  with  the 
liquid  thus  prepared.  Spread  the 
wet  paper  smoothly  on  a  piece  of 
tin,  e.g.  on  the  bottom  of  a  tin 
basin  (Fig.  148).  Press  the  nega- 
tive electrode  of  the  battery  against 
Fig.  148.  an  uncovered  part  of  the  tip.  Draw 

the    positive    electrode    over    the 

paper.  A  mark  is  produced  upon  the  paper  as  if  the  electrode  were 
wet  with  a  purple  ink.  In  this  case  the  potassium  iodide  is  decom- 
posed, and  the  iodide  combining  with  the  starch  forms  a  purplish- 
blue  compound. 

157.  (2)  Magnetic  Action  and  Magnetic  Field  of  a 
Straight  Current.  Magnetic  Lines  of  Force. 

Experiment  126.  —  Construct  a  low  resistance  battery  of  (say) 
four  cells.  Close  the  circuit  and  dip  the  wire  into  a  little  heap  of 
filings  of  soft  iron.  On  raising  the  wire  you  will  find  filings  adher- 
ing in  a  cluster  to  it  (Fig.  149). 


EFFECTS  PRODUCIBLE  BY  AN  ELECTRIC  CURRENT.    177 


If  a  wire  bearing  a  very  strong  current  be  passed  vertically  through 
the  center  of  a  board  on  which  have  been  sifted  some  very  fine  iron  fil- 
ings, the  filings  will  arrange  themselves  in  circular  lines  round  the 


Fig.  149. 

current-carrying  wire  (Fig.  150),  thus 
furnishing  a  graphic  representation  of 
the  magnetic  field  set  up  by  a  current. 
If  a  small  pocket  compass  be  carried 
around  and  near  the  wire,  the  needle 
will  at  every  point  take  a  position 
tangent  to  these  circular  lines  of  fil-  Fig.  150. 

ings,  whichever  way  the  current  passes. 

If  the  current  be  reversed,  however,  the  position  of  the  n  and  s  poles  of 
the  needle  will  be  reversed.  This  clearly  indicates  that  there  is  a  differ- 
ence of  direction  of  these  circular  lines  according  as  the  current  flows  in 
one  direction  or  in  the  other.  These  circular  lines  represent  the  so-called 
magnetic  lines  of  force  which  occupy  a  limited  space  or  field  round  a 
current-bearing  wire. 

158.    Deflection  of  the  Magnetic  Needle  by  a  Current. 

Experiment  127.  —  a.  Place  the  apparatus  ^(Fig.  151)  so  that  the 
magnetic  needle,  which  points  (nearly)  north  and  south,  shall  be 
parallel  with  the  wires  Wl  and  W2.  Introduce  the  +  electrode  of  a 
battery  into  screw-cup  T2,  and  the  —  electrode  into  screw-cup  Tv 
and  pass  a  current  through  the  upper  wire.  At  the  instant  the 
circuit  is  closed  the  needle  swings  on  its  axis,  and  after  a  few  oscilla- 
tions comes  to  rest  in  a  position  which  forms  an  angle  with  the  wire 
bearing  the  current. 

b.  Break  the  circuit  by  removing  one  of  the  wires  from  the  screw- 
cup.     The  needle,  under  the  influence  of  the  magnetic  action  of  the 
earth,  returns  to  its  original  position. 

c.  Reverse  the  current  by  inserting  the  +  electrode  of  the  battery 
into  screw-cup  Tx,  and  the  —  electrode  into  screw-cup  T2.     Again 


ITS 


ENERGY  OF  ELECTKIC  FLOW. 


there  is  a  deflection  of  the  needle,  but  the  direction  of  the  deflection 
is  reversed  ;  that  is,  the  north-pointing  pole  (N-pole),  which  before 
turned  to  the  west,  is  now  deflected  toward  the  east. 

d.    Place  your  right  hand  above  the  wire  with  the  palm  towards 


Fig.  151. 

the  wire,  and  with  the  fingers  pointing  in  the  same  direction  as  that 
in  which  the  current  is  flowing,  and  extend  your  thumb  at  right 
angles  to  the  direction  of  the  current  (Fig.  152).  You  observe  that 


Fig.  152.  — Right  hand  above  the  wire; 
needle  below  it. 


Fig.   153.  —  Right    hand   below   the 
wire  ;  needle  above  it. 


your  thumb  points  in  the  same  direction  as  the  N-pole  of  the  needle 
under  the  current-bearing  wire. 

e.  Reverse  the  current  again  (so  that  it  will  flow  northward),  place 
your  right  hand  as  before  (viz.  with  the  palm  towards  the  wire  and 
with  the  fingers  pointing  in  the  same  direction  as  the  current) ;  your 
outstretched  thumb  still  points  in  the  same  direction  as  the  N-pole  of 
the  needle. 


EFFECTS  PRODUCIBLE  BY  AN  ELECTRIC  CURRENT.    179 

/.  Introduce  the  +  electrode  of  the  battery  into  screw-cup  T3  and 
the  —  electrode  into  screw-cup  T4  so  that  the  current  will  flow  north- 
ward under  the  needle.  Place  the  right  hand  as  directed  before, 
except  that  it  must  be  under  the  wire,  so  that  the  wire  shall  be 
between  the  hand  and  the  needle  ;  the  thumb  will  point  in  the  same 
direction  as  the  N-pole  (Fig.  153).  Reverse  the  direction  of  the 
current  in  this  wire,  and  apply  the  same  test ;  the  same  rule  holds. 

The  rule  for  determining  the  direction  of  the  deflection 
of  the  N-poles  of  a  needle  when  the  direction  of  the 
current  is  known  is  this :  Place  the  outstretched  right  hand 
over  or  under  the  wire  so  that  the  wire  shall  be  between  the 
hand  and  the  needle,  with  the  palm  towards  the  needle,  the 
fingers  pointing  in  the  direction  of  the  current  and  the  thumb 
extended  laterally  at  right  angles  to  the  direction  of  the  cur- 
rent; then  the  extended  thumb  will  point  in  the  direction  of 
the  deflection  of  the  N-pole. 

It  will  be  observed  that  a  deflection  is  reversed  either 
by  reversing  the  current  or  by  changing  the  relative  posi- 
tions of  the  wire  and  needle,  e.g.  by  carrying  the  needle 
from  above  the  wire  to  a  position  below  it. 

The  force  exerted  by  the  current  upon  the  needle  in 
deflecting  it  is  called  an  electro-magnetic  force. 

159.    Simple  Galvaiioscope  or  Current  Detector. 

Experiment  128.  —  Introduce  the  +  electrode  of  the  battery  into 
screw-cup  T2  (Fig  151)  and  the  —  electrode  into  screw-cup  T3,  so 
that  the  current  will  pass  above  the  wire  in  one  direction  and  below 
it  in  the  opposite  direction,  as  indicated  by  the  arrows.  A  larger 
deflection  is  obtained  than  when  the  current  passes  the  needle  only  once. 

If  the  right-hand  test  be  applied,  it  will  be  seen  that 
the  tendency  of  the  current,  both  when  passing  the  needle 
in  one  direction  above  and  in  the  opposite  direction  below, 
is  to  produce  a  deflection  in  the  same  direction,  and  con- 


180          ENERGY  OF  ELECTRIC  FLOW. 

sequently  the  two  parts  of  the  current  assist  each  other 
in  producing  a  greater  deflection. 

If  a  more  sensitive  instrument,  i.e.  one  which  will 
produce  considerable  deflections  with  weak  currents,  be 
required,  then  it  will  be  necessary  to  pass  the  current 
through  an  insulated  wire  wound  many  times  around  the 
needle.  Such  an  instrument  is  called  a  galvanoscope  or 
current  detector,  since  one  of  its  important  uses  is  to  detect 
the  presence  of  a  current. 

16O.  Magnetizing-  Effect  of  an  Electric  Current. 
Electro-magnets. 

Experiment  129.  —  a.  Wind  an  insulated  copper  wire  in  the  form 
of  a  spiral  round  a  rod  of  soft  iron  (Fig.  154).  Pass  a  current  of 
electricity  through  the  spiral,  and  hold  an  iron  nail  near  the  end  of 
the  rod.  Observe,  from  its  attraction  for  the  nail,  that  the  rod  is 
magnetized.  A  magnet  may  be  provisionally  denned  as  a  body 
which  attracts  iron. 

b.  Break  the  circuit ;  the  rod  loses  its  magnetism  and  the  nail  drops. 

The  iron  rod  is  called  a  core,  the  coil  of  wire  a  helix,  and 
both  together  are  called  an  electro-magnet. 
In  order  to  take  advantage  of  the  attraction 
of  both  ends  or  poles  of  the  magnet,  the  rod 
is  most  frequently  bent  into  a  U-shape  (A, 
Fig.  155).  More  frequently  two  iron  rods 
are  used,  connected  by  a  rectangular  piece 
of  iron,  as  a  in  B  of  Figure  155.  The 
method  of  winding  is  such  that  if  the  iron 
core  of  the  U-magnet  were  straightened, 
or  the  two  spools  were  placed  together 
end  to  end,  one  would  appear  as  a  con- 
Fig.  154.  tinuation  of  the  other.  A  piece  of  soft 


EFFECTS  PRODUCIBLE  BY  AN  ELECTRIC  CURRENT.    181 

iron,  5,  placed  across  the  ends  and  attracted  by  them  is 
called  an  armature.     The  piece  of  iron  a  is  called  a  yoke. 

161.  (3)    Thermal    and     Luminous    Effects    of    the 
Electric  Current. 

Experiment  130. — Construct  a  low  resistance  battery  (§  181)  of 
four  to  six  cells,  and  introduce  into  the  circuit  a  platinum  wire,  No. 
30,  about  \  inch  long.  The  wire  very  quickly  becomes  white  hot,  i.e. 
it  emits  white  light,  which  indicates  a  temperature  of  approximately 
1900°  C. 

This  experiment  illustrates  the  conversion  of  the  energy 
of  an  electric  current  into  heat  energy.  In  this  case  the 
energy  of  the  current  is  said  to  be  consumed  in  over- 
coming the  resistance  which 
the  conductor  or  the  cir- 
cuit offers  to  its  passage. 
Heat  is  developed  by  a 
current  in  every  part  of 
the  circuit,  because  all 
substances  offer  some  resistance  to  a  current ;  in  other 
words,  there  are  no  perfect  conductors.  The  small  platinum 
wire  offers  much  greater  resistance  than  an  equal  length 
of  a  larger  copper  wire  ;  whence  the  greater  quantity  of 
heat  generated  in  this  part  of  the  circuit.  All  of  the 
energy  in  any  electric  current  that  is  not  consumed  in 
doing  other  kinds  of  work  is  changed  into  heat. 

162.  (4)    Physiological   Effects. 

Experiment  131.  —  Place  one  of  the  copper  electrodes  of  a  single 
voltaic  cell  on  each  side  of  the  tip  of  the  tongue.  A  slight  stinging 
(not  painful)  sensation  is  felt,  followed  by  a  peculiar  acrid  taste. 


182          ENEKGY  OF  ELECTRIC  FLOW. 


Section  III. 

ELECTRICAL  QUANTITIES  AND  UNITS. —OHM'S  LAW. 

163.  Strength    of   Current.      The  Ampere    and    the 
Coulomh.  —  The  magnitude  of  the  effects  produced  by  an 
electric  current  depends,  among  other  things,  upon  the 
magnitude  of  the  current.     Any  one  of  the  effects  pro- 
ducible by  a  current  may  be  made  the  basis  of  a  system  of 
measurement  of  currents.     For  example,  the  quantity  of 
hydrogen  gas  or  of  any  metal  liberated  at  the  cathode  in 
a  given  time,  by  electrolysis,  is  strictly  proportional  to  the 
magnitude  of  the  current,  or  as  it  is  technically  termed 
the  strength  of  the  current. 

By  current  strength  is  meant  the  number  of  units  of 
electricity  which  flows  in  a  given  time,  or,  briefly,  it  is 
the  "rate  of  flow."  The  practical  unit  of  current  (i.e.  the 
unit  of  current  strength)  is  the  ampere.  It  is  the  current 
which  passed  through  a  solution  of  nitrate  of  silver  (u  in 
accordance  with  standard  specifications  "),  deposits  silver 
at  the  rate  of  0.001118  gram  per  second.  The  quantity 
of  electricity  transferred  by  a  current  of  one  ampere  in 
one  second  is  called  a  coulomb.1  The  coulomb,  then,  is 
the  unit  of  quantity  of  electricity.  When  the  quantity 
of  electricity  conveyed  by  a  current  in  one  second  is  one 
coulomb,  its  strength  is  one  ampere. 

164.  Electro-Motive    Force.      The    Volt.   -       Water 
flows  from  one  place  to  another  in  virtue  of  a  difference 

1  The  definitions  of  the  coulomb  and  the  ampere  here  given  are  those  of  the  so- 
called  international  units,  which  were  adopted  as  the  legal  units  by  act  of  the  United 
States  Congress  in  July,  1864. 


ELECTRICAL   QUANTITIES    AND    UNITS.  183 

of  pressure  between  the  two  places,  and  the  flow  takes 
place  from  the  place  of  high  pressure  to  the  place  of  low 
pressure.  For  instance,  when  water  flows  from  a  reservoir 
or  cistern  the  pressure  at  any  point  in  the  pipe  is  due  to 
the  "head"  of  water  above  it.  If  it  be  set  flowing  by  a 
force  pump,  we  might  say  the  flow  of  water  is  due  to  a 
water-motive  force  which  could  be  expressed  as  equal  to 
a  "  head  "  of  a  certain  number  of  feet  of  water. 

Similarly,  electricity  flows  in  a  conductor  only  when 
there  is  a  difference  of  what  may  be  termed  electrical 
pressure  between  its  ends.  If  such  be  maintained  between 
two  points  connected  by  a  conductor,  it  obviously  repre- 
sents a  kind  of  current-producing  force,  one  which  can 
keep  electricity  in  motion  against  resistance.  It  is  for 
this  reason  called  electro-motive  force  (E.M.F.).  Electro- 
motive force  is  that  which  maintains  or  tends  to  maintain 
a  current  of  electricity  through  a  conductor.  That  which 
hinders  the  current  is  called  resistance. 

Difference  in  electrical  pressure  we  have  hitherto 
assumed  to  be  due  to  difference  of  potential.  It  is  this 
difference  of  electrical  pressure  which  sets  up  a  current  in 
the  conductor.  Potential  difference  may  be  due  to  con- 
tact of  dissimilar  substances,  as  in  the  voltaic  cell,  or  to 
the  movement  of  a  part  of  the  conductor  in  a  magnetic 
field,  as  in  the  dynamo  (p.  223). 

The  volt  is  the  name  chosen  for  the  practical  unit  of 
E.M.F.  and  difference  of  potential.  It  is  the  electrical 
pressure  required  to  maintain  a  current  of  one  ampere 
against  a  resistance  of  one  ohm  (§  165).  For  purposes 
where  great  accuracy  is  not  required,  it  will  answer  to 
consider  a  volt  as  the  E.M.F.  of  a  Daniell's  cell,  i.e.  it  is 


184  ENERGY  OF  ELECTRIC  FLOW. 

about  the  difference  of  potential  between  the  zinc  and 
copper  of  this  cell,  the  E.M.F.  of  a  standard  Daniell  cell 
being  approximately  1.07  volts. 

165.  Electrical    Resistance.       The    Ohm.   -   -   Every 
substance   offers   resistance   to  the  passage  of  a  current. 
Those  substances  which  offer  a  very  powerful  barrier  are 
called  insulators.    The  unit  of  resistance  is  called  the  ohm. 

The  international  ohm  is  "  the  resistance  offered  to  an 
unvarying  electric  current  by  a  column  of  mercury  at  the 
temperature  of  melting  ice,  14.421  grams  in  mass,  of  a 
constant  cross-sectional  area,  and  of  the  length  of  106.3 
centimeters  "  ;  or  about  the  resistance  of  9.3  ft.  of  No.  30 
(American  gauge)  copper  wire  (.01  in.  diam.). 

166.  Electrical  Work  and  Electrical  Power.      The 
Joule  and  the  Watt.  —  If  a  coulomb  of  electricity  flow 
between  two  points  in  a  conductor  whose   difference   of 
potential  is   one  volt,  then  one  joule  or  volt-coulomb  of 
work  is  done  thereby.     The  volt-coulomb  is  analogous  to 
the  foot-pound. 

If  a  conductor  be  traversed  by  a  current  of  one  ampere 
(i.e.  a  coulomb  per  second)  and  there  be  two  points  in  the 
conductor  whose  difference  of  potential  is  one  volt,  then 
the  rate  at  which  work  is  done  in  that  portion  is  one  watt 
=  one  joule  per  second.  The  joule  and  the  watt  are 
units  of  electrical  work  (or  energy)  and  electrical  power 
respectively. 

167.  Re'sume'.  —  A  unit  current  is  a  current  maintained 
by  a  unit  E.M.F.  against  a  unit  resistance. 

A  unit  E.M.F.  is  the  E.M.F.  required  to  maintain  a  unit 
current  against  a  unit  resistance. 


ELECTRICAL   QUANTITIES    AND    UNITS.  185 

A  conductor  has  a  unit  resistance  when  a  unit  E.M.F.  (or 
a  unit  difference  of  potential  between  its  two  ends)  causes  a 
unit  current  to  pass  through  it. 

A  unit  of  electric  power  is  the  power  of  a  unit  current 
maintained  by  a  unit  difference  of  potential. 

168.  Ohm's  L,aw.  —  The  three  factors,  current  (C), 
electro-motive  force  (E),  and  resistance  (R),  are  evidently 
interdependent.  Their  relations  to  one  another  are  stated 
in  the  well-known  Ohm's  Law  thus  :  The  current  is  equal 
to  the  electro-motive  force  divided  by  the  resistance;  or 

E  E 

C  =  77 ;  whence  E  =  R  C,  and  R  =  -^ 
it  u 

Hence  the  strength  of  a  current  is  directly  proportional  to 
the  E.M.F.  and  inversely  proportional  to  the  resistance. 
This  famous  law  is  the  basis  of  a  large  portion  of  electrical 
measurements  commonly  made.1 


EXERCISES. 

1.  What  E.M.F.  is  required  to  maintain  a  current  of  one  ampere 
against  a  resistance  of  one  ohm  ? 

2.  An  E.M.F.  of  10  volts  will  maintain  a  current  of  5  amperes 
against  what  resistance? 

3.  What  current  ought  an  E.M.F.  of  20  volts  to  maintain  against 
a  resistance  of  5  ohms? 

4.  A  volt-meter  applied  each  side  of  an  electric  lamp  shows  a 
difference  of  potential  of  40  volts  ;  what  current  flows  through  the 
lamp,  if  it  has  a  resistance  of  10  ohms  ? 

1  The  following  formulas  relating  to  the  electric  current  will  be  found  convenient 
for  reference  :    (1)  P  (watts)  =  C  (amperes)  x  E  (volts).      (2)  The  watt  OTIS  horse- 

O  F1 
power.    Hence— — =power  in  horse-power.     (3)  Substituting  in  (1)  the  value  of 

E2 

C  (Ohm's  formula),  we  have  P  =  — .     Or,  (4)  substituting  in  (1)  the  value  of  E  (Ohm's 

formula),  we  have  P  =  C*R. 


186 


ENERGY    OF    ELECTRIC    FLOW. 


5.  The  resistance  between  two  points  in  a  circuit  is  10  ohms.  An 
ammeter  (an  instrument  which  measures  the  strength  of  a  current  in 
amperes)  shows  that  there  is  a  current  strength  in  the  circuit  of  0.5 
ampere  ;  what  is  the  difference  in  potential  between  the  points  ? 


Section  IV. 


GALVANOMETER  COIL 


INSTRUMENTS    FOR    MEASUREMENT    OF   ELECTRIC 
CURRENTS. 

169.  Galvanometer.  —  This  is  an  instrument  for  meas- 
uring current-strength  by  means  of  the  deflection  of  a 
magnetic  needle  when  placed  in  the  field  of  the  current. 
It  is  so  constructed  that  either  the  deflection  angle  itself, 
or  some  function  of  it,  is  proportional  to  the  current- 
strength. 

A  very  simple  form  of  this  instrument  is  represented  in  sectional 

elevation  and  plan  in  Figure  156.  It 
consists  of  an  insulated  wire  wound 
many  times  around  a  magnetic 
needle.  A  card  graduated  like  that 
of  a  mariner's  compass  is  placed 
beneath  the  needle  so  that  the 
number  of  degrees  of  deflection  may 
be  read  from  it.  This  form  of 
instrument  is  much  used  to  detect 
the  presence  of  a  current,  to  locate 
faults,  etc. 

17O.  Tangent  Galvanom- 
eter. —  A  tangent  galvanom- 
eter is  one  so  constructed  that 
Fig.  ise.  the  current  passing  through 


MEASUREMENT    OF    ELECTRIC    CURRENTS. 


187 


it  is  proportional  to  the  tangent  of  the  angle  of  deflection 
produced.  To  this  end  it  is  necessary  that  the  needle  be 
very  short  (not  more  than  -fa)  in  comparison  with  the 
diameter  of  the  coil. 

It  consists  of  a  large  vertical  coil  (C,  Fig.  157)  in  the 
center  of  which  is  either  a  small  compass  needle  or  a 
needle  suspended  by  a  silk  fiber. 

A  needle  thus  placed  in  the  field  of  a  current  is  acted 
on  by  a  mechanical  couple  tending  to  place  it  at  right 
angles  to  the  plane  of  the  coil,  and  it  is  deflected  until 
this  couple  is  balanced  by  the  return  couple  due  to  the 
earth's  magnetism. 

When  the  scale  is  divided  into  degrees,  the  correspond- 
ing tangents  are  found  by  consulting  a  table  of  tangents 
(see  Appendix).  In  some  instru- 
ments the  scale  is  graduated  direct- 
ly in  tangents. 

If  the  strengths  of  two  currents 
are  to  be  compared,  it  is  only  nec- 
essary to  obtain  deflections  with 
each  current,  and  compare  the 
tangents  of  the  angles. 

171.  Ammeter.  —  If  the  gal- 
vanometer be  calibrated  so  as  to 
read  in  amperes,  we  shall  have  a 
direct^reading  ampere -meter,  or 
ammeter  as  it  is  more  commonly 
called.  There  is  a  great  variety 
of  ammeters  in  use,  for  a  description  of  which  the  student 
is  referred  to  technical  works  on  the  subject. 


Fig.    157. 


188          ENERGY  OF  ELECTRIC  FLOW. 


Section  V. 

RESISTANCE   OF   CONDUCTORS. 

172.  External  and  Internal  Resistance.  —  For  con- 
venience the  resistance  of  an  electric  circuit  is   divided 
into  two  parts,  the  external  and  the  internal.      External 
resistance  includes  all  the  resistance  of  a  circuit  except 
that  of  the  generator,  while  the  latter  is  termed  internal 
resistance. 

When  the  external  resistance  in  a  circuit  is  considered 
separately  from  the  internal,  Ohm's  formula  must  be  con- 
verted thus  (calling  the  former  R,  and  the  latter  r}:— 

r-    E 
~RT? 

If  a  cell  have  E  =  1  volt,  and  r  =  1  ohm,  and  the  con- 
necting wire  be  short  and  stout,  so  that  R  may  be  dis- 
regarded, then  the  cell  yields  a  current  of  one  ampere. 
If  by  any  means  the  internal  resistance  of  this  cell  can  be 
decreased  one-half,  it  will  then  be  capable  of  yielding  a 
two-ampere  current  under  the  same  conditions. 

173.  External  Resistance. 

Experiment  132.  —  Introduce  into  a  circuit  a  galvanometer,1  and 
note  the  number  of  degrees  the  needle  is  deflected.  Then  introduce 
into  the  same  circuit  the  wire  on  the  spool  numbered  4  on  the  plat- 
form 2  S  (Fig.  158).  (The  wire  on  any  one  of  the  five  spools  on  this 

1  The  galvanometer  represented  in  the  cut  is  a  form  of  galvanometer  chiefly  used 
hy  the  author  in  elementary  laboratory  work. 

2  The  platform  of  spools  containing  wire  of  different  (known)  sizes,  lengths,  and 
material,  so  arranged  that  any  one,  two,  or  more  can  he  introduced  into  the  circuit 
for  the  purpose  of  measurement  of  resistance,  is  an  instrument  of  great  convenience 
in  a  school  laboratory. 


RESISTANCE  OF  CONDUCTORS. 


189 


platform  can  at  any  time  be  introduced  into  a  circuit,  by  connecting 
the  battery  wires  with  the  binding  screws  on  each  side  of  the  spool 
to  be  introduced.) 

The  deflection  is  now  less  than  before.  The  copper  wire  on  this 
spool  is  16  yards  in  length  ;  its  size  is  No.  30  of  the  Brown  and 
Sharpe  wire  gauge.  When  this  spool  is  in  circuit,  the  circuit  is  16 


Fig.   158. 

yards  longer  than  when  the  spool  is  out.  The  effect  of  lengthening 
the  circuit  is  to  weaken  the  current,  as  shown  by  the  diminished 
deflection. 

Experiment  133.  —  Next,  substitute  Spool  2  for  Spool  4.  This 
contains  32  yards  of  the  same  kind  of  wire  as  that  on  Spool  4.  The 
deflection  is  still  smaller. 

The  weakening  of  the  current  by  introducing  these  wires  is  caused 
by  the  resistance  which  the  wires  offer  to  the  current,  much  as  the 
friction  between  water  and  the  interior  of  a  pipe  impedes,  to  some 
extent,  the  flow  of  water  through  it.  The  longer  the  pipe  the  greater 
is  the  resistance  to  the  flow. 

If  the  wire  on  the  spools  had  been  the  only  resistance  in  the  cir- 
cuit, then,  when  Spool  2  was  in  the  circuit,  the  resistance  would  have 
been  double  what  it  was  when  Spool  4  was  in  the  circuit,  and  the 
current,  with  double  the  resistance,  would  have  been  half  as  strong. 

(1)  Other  things  being  equal,  the  resistance  of  a  conductor 
varies  as  its  length. 


190          ENERGY  OF  ELECTRIC  FLOW. 

Experiment  134.  —  Next  substitute  Spool  1  for  Spool  2.  This 
spool  contains  32  yards  of  No.  23  copper  wire,  —  a  thicker  wire  than 
that  on  Spool  2,  but  the  length  of  the  wire  is  the  same.  The  deflec- 
tion is  now  greater  than  it  was  when  Spool  2  was  in  circuit.  This 
indicates  that  the  larger  wire  offers  less  resistance. 

Careful  experiments  show  that  (2)  the  resistance  of  all 
conductors  varies  inversely  as  the  areas  of  their  cross-sections. 
If  the  conductors  be  cylindrical,  it  varies  inversely  as  the 
squares  of  their  diameters. 

Experiment  135.  —  Substitute  Spool  5  for  Spool  1,  and  compare 
the  deflection  with  that  obtained  when  Spool  4  was  in  the  circuit. 
The  deflection  is  smaller  than  when  Spool  4  was  in  circuit.  The 
wire  on  these  two  spools  is  of  the  same  length  and  size,  but  the  wire 
of  Spool  5  is  German-silver.  It  thus  appears  that  German-silver 
offers  more  resistance  than  copper. 

(3)  In  obtaining  the  resistance  of  a  conductor,  the  specific 
resistance  of  the  substance  must  enter  into  the  calculation. 
(See  table  of  specific  resistances  in  the  Appendix.) 

The  resistance  of  metal  conductors  increases  slowly 
with  the  temperature  of  the  conductor.  The  resistance  of 
German-silver  is  affected  less  by  changes  of  temperature 
than  that  of  most  metals ;  hence  its  general  use  in 
standards  of  resistance. 

174.    Internal  Resistance. 

Experiment  136.  —  Connect  with  the  galvanometer  the  copper 
and  zinc  strips  used  in  Experiment  -122,  and  introduce  the  strips  into 
a  tumbler  nearly  full  of  acidulated  water.  Note  the  deflection. 
Then  raise  the  strips,  keeping  them  the  same  distance  apart,  so  that 
less  and  less  of  the  strips  will  be  submerged.  As  the  strips  are 
raised,  the  deflection  becomes  smaller.  This  is  caused  by  the 
increase  of  resistance  in  the  liquid  part  of  the  circuit,  as  the  cross- 
section  of  the  liquid  lying  between  the  two  strips  becomes  smaller. 


MEASUREMENT    OF    RESISTANCE. 


191 


(4)  The  internal  resistance  of  a  circuit,  other  things  being 
equal,  varies  inversely  as  the  area  of  the  cross-section  of  the 
liquid  between  the  two  elements. 

In  a  large  cell  the  area  of  the  cross-section  of  the  liquid 
between  the  elements  is  larger  than  in  a  small  cell,  con- 
sequently the  internal  resistance  is  less.  This  is  the  only 
way  in  which  the  size  of  the  cell  affects  the  current. 

Obviously  the  resistance  of  the  battery  would  be  increased  by  any 
increase  of  the  distance  between  the  elements,  since  this  increases  the 
length  of  the  liquid  conductor ;  but  as  this  distance  is  usually  made  as 
small  as  convenient,  and  is  kept  invariable,  it  demands  little  of  our 
attention. 


Section  VI. 

MEASUREMENT  OF  RESISTANCE. 

1 75.    Description  of  the  Resistance  Box. 

Figure  159  represents  a  wooden  box  containing  what  is  equivalent  to  a 
series  of  coils  of  German-silver  wire,  whose  resistance  ranges  from  0.1  ohm 
to  100  ohms.     Each  of 
these  coils  is  connected 
with  a  brass  stud  on  the 
top  of  the  box. 

Three  switches,  A, 
B,  and  C,  so  connect 
the  coils  with  the  bind- 
ing screws  a  and  6  that 
a  current  can  be  sent 
through  any  three  coils 
at  the  same  time  by 
moving  the  switches  on 
to  the  proper  studs. 
The  resistance  in  ohms  of  each  coil  is  marked  on  the  box  near  its  stud. 


192 


ENERGY  OF  ELECTRIC  FLOW. 


When  the  three  switches  rest  upon  studs  marked  0,  the  current  meets 
with  no  appreciable  resistance  in  passing  through  the  box,  but  any 
desired  resistance  within  the  range  of  the  instrument  can  be  introduced 
by  moving  the 'switches  on  to  the  studs,  the  sum  of  whose  resistances  is 
the  resistance  required.  This  instrument  we  shall  call  a  resistance  box. 


G    G    X 


Fig.  160. 


176.    Wheatstone  Bridge. 

Figure  160  represents  a  perspective  view  of  the  bridge  (as  modified  by 
the  author),  and  Figure  161  represents  a  diagram  of  the  essential  electri- 
cal connections.  The  battery  wires  are  connected  with  the  bridge  at  the 

binding  screws  B  B'.  A  gal- 
vanometer, G,  is  connected  at 
G  G',  a  resistance  box,  r,  at 
R  R,  and  the  conductor,  x, 
whose  resistance  is  sought,  at 
XX. 

When  the  circuit  is  closed 
by  means  of  the  key  T,  the 
current,  we  will  suppose, 
enters  at  B  ;  on  reaching  the  point  A  it  divides,  one  part  flowing  via  the 
branch  A  G  B',  and  the  other  via  the  branch  A  D  B'.  If  points  D  and  G 
in  the  two  branches  be  at 
different  potentials  and  a 
connection  be  made  between 
them  through  the  galvanom- 
eter, G,  by  closing  the  key 
S,  there  will  be  a  current 
through  this  wire  and  through 
the  galvanometer,  and  a  de- 
flection of  the  needle  will  be 
produced.  But  if  the  points 
D  and  G  be  at  the  same 
potential,  there  will  be  no 
cross  current  through  the 
bridge  wire  and  no  deflection. 
Now  it  can  be  demonstrated 
that  points  D  and  G  will  be  at 
the  same  potential  when  R 
(the  resistance)  of  A  D  :  R  of  D  B7  ::  R  of  A  G  :  R  (the  unknown  resist- 
ance) of  G  B'.  Between  A  and  T)  and  A  and  G  there  are  three  coils  of 


MEASUREMENT    OF    RESISTANCE.  193 

wire  having  resistances  respectively  of  1,  10,  and  100  ohms.  One  or 
more  of  these  coils  are  introduced  into  the  circuit  by  removing  the 
corresponding  plugs  a,  6,  c,  d,  e,  and  /.  As  the  other  connections 
between  A  and  D,  and  A  and  G,  have  no  appreciable  resistance,  being 
for  the  most  part  short  brass  bars,  the  only  practical  resistance  between 
these  points  is  that  introduced  at  will  through  the  coils.  Similarly 
between  points  D  and  B',  the  only  practical  resistance  is  that  introduced 
at  will  through  the  resistance  box,  and  between  the  points  G  and  B'  the 
resistance  is  the  resistance  (x)  sought. 

It  is  apparent,  then,  that  in  using  the  bridge  after  the  connections  are 
properly  made  through  the  several  instruments  and  certain  known 
resistances  are  introduced  between  A  and  D,  and  A  and  G,  we  have 
simply  to  regulate  the  resistance  through  the  resistance  box  so  that  there 
will  be  no  deflection  in  the  galvanometer;  then  we  are  sure  that  the 
above  proportion  is  true.  The  first  three  terms  of  the  proportion  being 
known,  the  fourth  term,  which  is  the  resistance  sought,  is  computable.1 

If  the  same  resistance  be  introduced  between  points  A  and  G  as 
between  A  and  D,  it  is  evident  that  the  resistance  in  the  resistance  box  r 
must  be  made  equal  to  the  unknown  resistance  x  in  order  that  there  may 
be  no  deflection  in  the  galvanometer.  Consequently  when  this  result  is 
obtained  the  resistance  of  x  may  be  read  from  the  resistance  box. 

Experiment  137.  —  Measure  the  resistance  of  each  of  the  several 
spools  of  wire  used  above,  —  electro-magnets,  electric  lamps,  etc.,  — 
using  the  bridge.  Place  the  switches  of  the  resistance  box  on  the 
zero  studs.  Make  connections  as  in  the  description  above.  Then 
close  the  circuit  at  T,  and  afterwards  the  bridge  at  S.  There  will 
probably  be  a  deflection  in  the  galvanometer,  Regulate  the  resist- 
ance through  the  resistance  box,  throwing  in  or  taking  out  resistance 
according  as  one  or  the  other  tends  to  reduce  the  deflection  (the 
process  is  much  like  that  of  weighing),  until  there  is  no  deflection. 
Then  compute  the  resistance  sought  according  to  the  above  proportion. 

• 

1  The  accuracy  of  the  results  obtained  largely  depends  upon  so  choosing  resist- 
ances of  the  bridge  as  to  make  the  arrangement  have  maximum  sensibility,  and  upon 
the  sensitiveness  of  the  galvanometer.  In  using  the  bridge  the  following  directions 
should  be  observed  :  (1)  Always  close  the  circuit  at  T  before  closing  the  bridge  at  S, 
and  in  breaking  the  circuit  reverse  this  order.  (2)  Introduce  between  A  and  D,  and 
A  and  G,  resistance  as  nearly  equal  to  the  resistance  sought  (x)  as  practicable.  If 
you  have  no  conception  what  the  unknown  resistance  is,  it  is  best  to  begin  by  using 
high  resistances.  (3)  Use  a  sensitive  galvanometer,  e.g.  a  mirror  galvanometer,  or 
the  galvanometer  shown  in  Figure  158,  substituting  the  astatic  needle  for  the  tangent 
needle. 


194 


ENERGY  OF  ELECTRIC  FLOW. 


B' 


177.    Measurement    of     Galvanometer     Resistance. 
Lord  Kelvin's  Method. 

The  bridge  may  be  used  for  measuring 
the  resistance  of  the  galvanometer  actually 
in  use.  The  bridge  is  arranged  as  in  Figure 
162.  The  resistance  in  the  resistance  box 
K  is  then  varied  until  the  deflection  of  G 
does  not  change  when  the  key  S  is  closed  ; 
then 


in  which  r  is  the  resistance  of  the  galva- 
nometer, R  is  the  resistance  in  the  resistance 
box,  and  a  and  6  are  the  resistances  in 
the  arms  A  G'  and  A  D  respectively.  If 
Fig.  162.  a  =  6,  then  r  =  R. 


Section  VII. 

E.M.F.    OF    DIFFERENT    CELLS.  —  DIVIDED    CIRCUITS.— 
METHODS  OF  COMBINING  VOLTAIC  CELLS. 

178.    Electro-Motive  Force  of  Different   Cells.  —  If 

a  galvanometer  be  introduced  into  a  circuit  with  different 
battery  cells,  e.g.  Bunsen,  Daniell,  Greiiet,  etc.,  very 
different  deflections  will  be  obtained,  showing  that  the 
different  cells  yield  currents  of  different  strengths.  This 
may  be  in  some  measure  due  to  a  difference  in  their 
internal  resistance,  but  it  is  chiefly  due  to  the  difference 
in  their  electro-motive  forces.  We  have  learned  that 
difference  of  electro-motive  force  is  due  to  the  difference 
of  the  chemical  action  on  the  two  plates  used,  and  this 
depends  upon  the  nature  of  the  substances  used.  It  is 


E.M.F.    OF    DIFFERENT    CELLS,    ETC.  195 

wholly  independent  of  the  size  of  the  plates  ;  hence  the 
electro-motive  force  of  a  large  battery  cell  is  no  greater 
than  that  of  a  small  one  of  the  same  kind.  Consequently 
any  difference  in  strength  of  current  yielded  by  battery 
cells  of  the  same  kind,  but  of  different  sizes,  is  due  wholly 
to  a  difference  in  their  internal  resistances. 

The  electro-motive  forces  of  the  Bunsen,  Daniell,  and 
Grenet  cells  are  respectively  about  1.8,  1,  and  2  volts. 

179.    Divided  Circuits;    Shunts. 

Experiment    138.  —  Make   a   divided   circuit  as 
in  Figure  163  (using  double   connectors  a  and  5). 
Insert   a   galvanometer,    G,    in    one    branch   and   a 
resistance   box,    R,    in   the   other.     When   the   cur- 
rent reaches  a,  it  divides,  a  portion  traversing  one 
branch  through  the  galvanometer,  and  the  remainder 
passing  through  the  other  branch  and  the  resistance         FIs- 163' 
box.     The  branch  a  R  b  is  called  a  shunt  or  derived  circuit.     Increase 
gradually  the  resistance  in  the  resistance  box.     The  result  is  that 
it  throws  more  of  the  current  through  the  galvanometer,  as  shown 
by  the  increase  of  deflection. 

In  a  divided  circuit  the  current  divides  between  the  paths 
inversely  as  their  resistances.  For  example,  if  the  resist- 
ance of  the  resistance  box  above  be  4  ohms,  and  the 
resistance  in  the  galvanometer  be  1  ohm,  then  four-fifths 
of  the  current  will  traverse  the  latter  and  one-fifth  the 
former. 

Suppose  that  the  resistance  box  and  galvanometer  be 
removed  from  the  shunts,  and  that  the  shunts  be  of  the 
same  length,  size,  and  kind  of  wire,  and  consequently 
have  equal  resistances.  Using  the  two  wires  instead  of 
one  to  connect  a  and  b  is  equivalent  to  doubling  the  size 
of  this  portion  of  the  conductor ;  consequently  the  re- 
sistance of  this  portion  is  reduced  one-half. 


196          ENERGY  OF  ELECTRIC  FLOW. 

Generally,  the  joint  resistance  of  two  branches  of  a  circuit 
is  the  product  of  their  respective  resistances  divided  by  their 
sum. 

If  any  portion  of  a  circuit  be  divided  into  three  or  more 
branches  whose  resistances  are  respectively  rv  r%,  r^  etc., 
it  may  be  demonstrated  1  that, 

E^n^^n"* 

in  wliich  R  represents  the  joint  resistance  of  the  several 
branches.  That  is,  the  reciprocal  of  the  joint  resistance  of 
any  number  of  branches  is  equal  to  the  sum  of  the  reciprocals 
of  the  resistances  of  the  several  branches. 

ISO.  Combining-  Cells.     Batteries. 

A  number  of  cells  connected  in  such  a  manner  that  the 
currents  generated  by  all  have  the  same  direc- 
tion constitutes  a  voltaic  battery.  The  object 
of  combining  cells  is  to  get  a  stronger  current 
than  one  cell  will  afford.  We  learn  from 
Ohm's  law  that  there  are  two,  and  only  two, 
ways  of  increasing  the  strength  of  a  current. 
It  must  be  done  either  by  increasing  the 
E.M.F.  or  by  decreasing  the  resistance.  So 
we  combine  cells  into  batteries,  either  to  secure 
greater  E.M.F.  or  to  diminish  the  internal  re- 
sistance. Unfortunately,  both  purposes  cannot 
y  be  accomplished  by  the  same  method. 

I  181.    Batteries   of  Low   Internal   Resist- 

ance. —  Figure    164    represents    three    cells 
Fig.  164.       having  all  the  carbon  (-}-)  plates  electrically 

i  See  the  author's  Principles  of  Physics,  p.  509. 


'  °i 

if 
\( 


E.M.F.    OF    DIFFERENT    CELLS,    ETC.  197 

connected  with  one  another,  and  all  the  zinc  ( — )  plates 
connected  with  one  another,  and  the  triplet  carbons  are 
connected  with  the  triplet  zincs  by  the  leading-out  wires 
through  a  galvanometer  G. 

It  is  easy  to  see  that  through  the  battery  the  circuit 
is  divided  into  three  parts,  and  consequently  the  conduc- 
tivity in  this  part  of  the  circuit,  according  to  the  principle 
stated  in  §  179,  must  be  increased  threefold  ;  in  other 
words,  the  internal  resistance  of  the  three  cells  is  one-third 
of  that  of  a  single  cell.  This  is  called  connecting  cells 
"  in  multiple  arc,"  and  the  battery  is  called  a  "  battery  of 
low  internal  resistance."  The  resistance  of  the  battery  is 
decreased  as  many  times  as  there  are  cells  connected  in 
multiple  are,  but  the  E.M.F.  is  that  of  one  cell  only. 

The    formula   for  the  current-strength  in  this  case  is 

written  thus  : 

E 


in  which  n  represents  the  number  of  cells.  It  is  evident 
from  this  formula  that  when  R  is  so  great  that  -  is  a 

v  7Z* 

small  part  of  the  whole  resistance  of  the  circuit,  little  is 
added  to  the  value  of  C  by  increasing  the  number  of  cells 
in  multiple  arc. 

182.  Batteries  of  High  Internal  Resistance  and 
Great  E.M.F.  —  Figure  165  represents  four  cells  having 
the  carbon  or  -|-  plate  of  one  connected  with  the  zinc  or  — 
plate  of  the  next,  and  the  -j-  plate  at  one  end  of  the  series 
connected  by  leading-out  wires  through  a  galvanometer 
with  the  —  plate  at  the  other  end  of  the  series.  It  is  evi- 


198  ENERGY  OF  ELECTRIC  FLOW. 

dent  that  the  current  in  this  series  traverses  the  liquid 
four  times,  which  is  equivalent  to  lengthening  the  liquid 

conductor  four  times,  and  of 
course  increasing  the  internal 
resistance    fourfold.     But, 
while  the  internal  resistance 
|+  is  increased,  the  E.M.F.  of 
the    battery    is    increased    as 
Fig.  165.  many  times  as  there  are  cells 

in  series.  The  gain  by  increasing  the  E.M.F.  more  than 
offsets,  in  many  cases  (always  when  the  internal  resistance 
is  a  small  part  of  the  whole  resistance  of  the  circuit),  the 
loss  occasioned  by  increased  resistance. 

The  formula  for  current-strength  in  this  case  becomes 

XV,       T? 

c== 


It  is  evident  that  C  is  increased  most  by  adding  cells  in 
series  when  n  r  is  smallest  in  comparison  with  R. 

183.    Rule  for  Combining-  Cells. 

When  the  external  resistance  is  large,  connect  cells  in 
series  ;  when  the  external  is  less  than  the  internal  resistance, 
connect  cells  in  multiple  arc. 

EXERCISES. 

1.  What  E.M.F.  is  required  to  maintain  a  current  of  one  ampere 
through  a  resistance  of  one  ohm  ? 

2.  Through  what  resistance  will  an  E.M.F.  of  ten  volts  maintain 
a  current  of  5  amperes  ? 

3.  What  current  ought  an  E.M.F.  of  20  volts  to  maintain  through 
a  resistance  of  5  ohms  ? 


EXERCISES.  199 

4.  A  voltmeter  applied  each  side  of  an  electric  lamp  shows  a  differ- 
ence of  potential  of  40  volts  ;  "what  current  flows  through  the  lamp, 
if  it  have  a  resistance  of  10  ohms  ? 

5.  The  resistance  between  two  points  in  a   circuit  is  10   ohms. 
An  ammeter  shows  that  there  is  a  current-strength  in  the  circuit  of 
0.5  ampere  ;  what  is  the  difference  in  potential  between  the  points  ? 

6.  What  current  will  a  Bunsen  cell  furnish  when  r  =  0.9   ohm 
(about  the  resistance  of  a  quart  cell),  E  =  1.8  volts,  and  R  =  0.01 
ohm  (about  the  resistance  of  3  ft.  of  No.  16  wire)  ? 

[In  the  following  exercises,  whenever  a  Bunsen  cell  is  mentioned 
it  may  be  understood  to  be  a  quart  cell,  having  a  resistance  of  about 
0.9  ohm.  Its  E.M.F.  is  about  1.8  volts.] 

7.  a.  When  is  a  large  cell  considerably  better  than  a  small  one  ? 
b.  When   does   the   size   of   the   cell  make  little  difference  in  the 
current  ? 

8.  If  you  have  a  dozen  quart  cells,   how  can  you  make  them 
equivalent  to  one  3-gallon  cell  ? 

9.  If  a  battery  of  10  cells  have  an  E.M.F.  10  times  greater  than 
that  of  a  single  cell,  why  will  not  the  battery  yield  a  current  ten 
times  as  strong  ? 

10.  a.  The  internal  resistance  of  ten  cells,  connected  in  multiple 
arc,  is  what  part  of  that  of  a  single  cell  ?     b.  If  the  cells  were  con- 
nected in  series,  how  would  the  resistance  of  the  battery  compare 
with  that  of  one  of  its  cells  ?     c.  How  would  the  E.M.F.  of  the  latter 
battery  compare  with  that  of  a  single  cell  ? 

11.  What  current  will  a  single  Bunsen  cell  furnish  through  an 
external  resistance  of  10  ohms  ? 

12.  What  current  will  8  Bunsen  cells,  in  series,  furnish  through 
the  same  resistance  ? 

SOLUT.ON  :  =          ~~  =  0.83+  ampere. 


13.  What  current  will  8  Bunsen  cells,  in  multiple  arc,  furnish 
through  the  same  external  resistance  ? 


14.  What  current  will  a  Bunsen  cell  furnish  through  an  external 
resistance  of  0.4  ohm  ? 


200  ENERGY   OF   ELECTRIC   FLOW. 

15.  What  current  will  a  battery  of  two  Bunsen  cells,  in  series, 
furnish  through  the  same  resistance  as  the  last  ? 

16.  What  current  will  two  cells,  in  multiple  arc,  furnish  through 
the  same  resistance  ? 

17.  A  coil  of  wire  having  a  resistance  of  10  ohms  carries  a  current 
of  1.5  amperes.     Required  the  difference  of  potential  at  its  ends. 

18.  a.  The  resistance  between  two  points,  A  and  B,  of  a  con- 
ductor is  2.5  ohms  ;   the  resistance  of  a  shunt  between  the  same 
points  is  1.5  ohms  ;  what  is  the  joint  resistance  between  these  points? 
b.  If  a  current  of  10  amperes  be  maintained  between  these  points, 
what  will  be  the  strength  of  current  in  each  branch  ?     c.  How  will 
the  strength  of  current  between  these  points  be  affected  if  the  shunt 
be  removed  and  the  same  fall  of  potential  be  preserved  ?     Why  ? 


Section  VIII. 

MAGNETS    AND   MAGNETISM. 

184.  Law  of  Magnets.  —  Suspend  by  fine  threads  in 
a  horizontal  position  two  stout  darning-needles  which 
have  been  drawn  in  the  same  direction  (e.g.  from  eye  to 
point)  several  times  over  the  same  pole  of  a  powerful 
electro-magnet.  These  needles,  separated  a  few  feet  from 
each  other,  take  positions  parallel  with  each  other,  and 
both  lie  in  a  northerly  and  southerly  direction  with  the 
points  of  each  turned  in  the  same  direction. 

That  point  in  the  Arctic  zone  of  the  earth  towards 
which  magnetic  needles  point  is  called  the  north  magnetic 
pole  of  the  earth.  That  end  of  a  needle  which  points 
toward  the  north  magnetic  pole  of  the  earth  is  called  the 
north-seeking,  marked,  or  -\-pole;  this  is  the  end  that  is 


MAGNETS    AND    MAGNETISM.  201 

always  marked  for  the  purpose  of  distinguishing  one  from 
the  other.  That  end  of  the  needle  which  points  south- 
ward is  called  the  south-seeking,  unmarked,  or — pole. 

Experiment  139.  —  Bring  both  points  near  each  other  ;  there  is 
a  mutual  repulsion.  Bring  both  eyes  near  each  other  ;  there  is  a 
mutual  repulsion.  Bring  a  point  and  an  eye  near  each  other  ;  there 
is  a  mutual  attraction. 

Like  poles  of  magnets  repel,  unlike  poles  attract  each  other. 

185.    Magnetic  Transparency  and  Induction. 

Experiment  140.  —  Interpose  a  piece  of  glass,  paper,  or  wood- 
shaving  between  the  two  magnets.  These  substances  are  not  them- 
selves perceptibly  affected  by  the  magnets,  nor  do  they  in  the  least 
affect  the  attraction  or  repulsion  between  the  two  magnets. 

Substances  that  are  not  susceptible  to  magnetism  are 
said  to  be  magnetically  transparent.  When  a  magnet  causes 
another  body,  in  contact  with  it  or  in  its  neighborhood, 
to  become  a  magnet,  it  is  said  to  induce  magnetism  in  that 


Fig.  166. 

body.  As  attraction,  and  never  repulsion,  occurs  between 
a  magnet  and  an  unmagnetized  piece  of  iron  or  steel,  it 
must  be  that  the  magnetism  induced  in  the  latter  is  such 
that  opposite  poles  are  adjacent :  that  is,  a  N  or  -f-  pole 
induces  a  S  or  —  pole  next  itself,  as  shown  in  Figure 
166. 

186.    Polarity. 

Experiment  141.  —  Strew  iron  filings  on  a  flat  surface,  and  lay 
a  bar  magnet  on  them.    On  raising  the  magnet  it  is  found  that  large 


202  ENERGY    OF    ELECTRIC    FLOW. 

tufts  of  filings  cling  to  the  poles,  as  in  Figure  167,  especially 
to  the  edges  ;  but  the  tufts  diminish  regularly  in  size  from 
each  pole  towards  the  center,  where  none  are  found. 

Magnetic  attraction  is  greatest  at  the  poles,  and 
diminishes  towards  the  center,  where  it  is  nothing; 
i.e.  the  center  of  the  bar  is  neutral.  This  dual 
character  of  the  magnet,  as  exhibited  at  its  opposite 
extremities,  is  called  polarity.  If  a  magnet  be 
broken,  each  piece  becomes  a  magnet  with  two 
poles  and  a  neutral  line  of  its  own. 

187.    Retentivity  and  Resistance. 

It  is  more  difficult  to  magnetize  steel  then  iron ; 
on  the  other  hand,  it  is  difficult  to  demagnetize  steel, 
while  soft  iron  loses  nearly  all  its  magnetism  as  soon  as 
it  is  removed  from  the  influence  of  the  inducing  body. 
That  quality  of  steel  by  which  it  resists  the  escape  of 
magnetism  which  it  has  once  acquired  is  called  its  reten- 
tivity. The  greater  the  retentivity  of  a  magnetizable  body, 
the  greater  is  the  resistance  which  it  offers  to  becoming 
magnetized.  The  harder  steel  is,  the  greater  is  its  retentivity. 
Hence,  highly  tempered  steel  is  used  for  permanent  mag- 
nets. Hardened  iron  possesses  considerable  retentivity  ; 
hence  the  cores  of  electro-magnets  should  be  made  of  the 
softest  iron,  that  they  may  acquire  and  part  with  magnetism 
instantaneously. 

188.  Forms  of  Artificial  Magnets.  —  Artificial  magnets, 
including  permanent  magnets  and  electro-magnets,  are  usually  made  in 
the  shape  either  of  a  straight  bar  or  of  the  letter  U,  according  to  the  use 
to  be  made  of  them.  If  we  wish,  as  in  the  experiments  already  described, 
to  use  but  a  single  pole,  it  is  desirable  to  have  the  other  as  far  away  as 
possible ;  then,  obviously,  the  bar  magnet  is  most  convenient.  But  if 


LINES  OF  MAGNETIC  FORCE. 


203 


the  magnet  is  to  be  used  for  lifting  or  holding  weights,  the  U-form  (see 
Fig.  155)  is  far  better,  because  the  attraction  of  both  poles  is  conveniently 
available. 


Section  IX. 

LINES    OF   MAGNETIC   FORCE.  —  THE   MAGNETIC   CIRCUIT. 

189.  Lines  of  Magnetic  Force.  —  These  lines  are 
easily  studied  by  the  use  of  iron  filings.  The  field  of 
force  around  a  magnet  is  shown  by  placing  a  paper  over 


Fig.  168. 

it,  dusting  filings  upon  the  paper,  and  tapping  it.  The 
filings  take  symmetrical  positions,  form  curves  between 
the  poles  of  the  magnet  or  magnets,  and  show  that  the 
lines  of  force  connect  the  opposite  poles  of  the  magnet.  The 
fact  is,  that  each  filing,  when  brought  within  the  influence 


204 


ENERGY  OF  ELECTRIC  FLOW. 


of  the  magnetic  field,1  becomes  a  magnet  by  induction, 
and  of  necessity  tends  to  take  a  definite  position  which 
represents  the  resultant  of  the  forces  acting  upon  it  from 


;:>/l\\<:<::  5^ 

/    ;   \  \X .--— '  W 


Fig.  169. 


each  pole  of  the  system.  A  line  of  magnetic  force  is  a  line 
drawn  in  such  a  manner  that  the  tangent  to  it  at  any 
point  indicates  the  direction  of  the  resultant  magnetic 


^~^//p\M$ 
N::---X///  vi\\N 

x^  **•'/!  \        \     \     \ 

.    ---^"-     /    /        !     ;  \  ^ 


Fig.  17O. 

force  at  that  point.  Figure  168  represents  a  magnetic 
field  photographed  from  a  specimen  paper,  and  Figure  169 
is  a  graphical  representation  of  the  same.  In  this  illustra- 

1 A  portion  of  space  throughout  which  magnetic  effects  are  exerted  is  called  a 
magnetic  field. 


LINES    OF    MAGNETIC    FORCE. 


205 


Fig.  171. 


tion  the  unlike  poles  of  two  magnets  are  placed  opposite 
each  other.  Figure  170  is  a  diagram  of  paths  of  lines  of 
force  of  a  bar  magnet,  and  Figure  171  of  a  U-shaped  magnet. 

19O.     Magnetic     Circuit.  -  -  A 

line  of  force  is  assumed  arbitrarily 
to  start  from  the  N-pole  and  to  pass 
through  the  surrounding  medium 
(e.g.  the  air),  entering  the  magnet 
by  the  S-pole,  and  completing  its 
path  through  the  magnet  itself  to  ^ 
its  starting-point  (the  N-pole),  thus  '^ 
forming  a  complete  circuit  (Fig.  / , 
170).  These  lines  do  not  all  ( 
emerge,  however,  from  the  extrem- 
ities. A  multitude  of  lines  start 
from  all  parts  of  the  magnet  and 
enter  at  corresponding  points  on  the  other  side  of  its 
central  or  neutral  line.  No  magnetic  line  of  force  can 
exist  without  completing  its  own  circuit,  and  lines  of  force 
never  cross  or  merge  into  one  another,  consequently  a 
magnet  cannot  have  a  single  pole. 

Lines  of  force  possess  several  peculiar  characteristics.  One  is  that  in 
air  and  most  other  mediums  they  tend  to  separate  from  one  another,  but 
at  the  same  time  tend  to  become  as  short  as  possible.  The  strain  is  as  if 
these  lines  were  stretched  elastic  threads  endowed  with  the  property  of 
repelling  one  another  as  well  as  of  shortening  themselves;  in  other  words, 
there  is  tension  along  the  lines  and  pressure  at  right  angles  to  them.  If 
the  N-pole  of  one  magnet  be  placed  opposite  the  S-pole  of  another  (Fig. 
169),  the  lines  of  force  issuing  from  the  former  will  enter  the  latter,  and, 
tending  to  shorten,  will  produce  attraction.  If  the  similar  ends  be  opposed 
(Fig.  172),  the  lines  of  force  will  be  turned  away  from  each  pole  in  all 
directions,  and  will  complete  their  circuits  independently.  Thus  becom- 
ing parallel  they  will  repel  one  another ;  for  this  reason  like  magnetic 
poles  repel  each  other. 


206 


ENERGY    OF    ELECTRIC    FLOW. 


Air  is  a  poor  conductor  for  lines  of  force,  or  its  permeability  is  low ; 
on  the  other  hand,  iron  has  high  permeability  for  lines  of  force,  and  if  a 
piece  of  iron  be  brought  within  a  magnetic  field,  a  portion  of  the  lines  of 


Fig.  173. 

force  will  crowd  together  into  it,  leaving  their  normal  paths  through  the 
air  for  a  medium  of  greater  permeability. 

191.  Law  of  Inverse  Squares.  —  It  may  be  demon- 
strated experimentally1  that  the  force  exerted  between  two 
magnetic  poles  varies  inversely  as  the  square  of  the  distance 
between  them. 


Section  X. 

TERRESTRIAL   MAGNETISM. 

192.    The  Earth  a  Magnet. 

Experiment  142.  —  Place  a  dipping-needle  2  over  the  +  pole  of  a 
bar  magnet  (Fig.  173).  The  needle  takes  a  vertical  position  with 
its  —  pole  down.  Slide  the  supporting  stand  along  the  bar  ;  the 

—  pole  gradually  rises 
until  the  stand  reaches 
the  middle  of  the  bar, 
where  the  needle  becomes 
horizontal.  Continue 
.Fig.  173.  moving  the  stand  toward 

1  See  tlie  author's  Principles  of  Physics,  p.  528. 

2  A  magnetic  needle  so  supported  that  it  can  rotate  in  a  vertical  plane  is  called  a 
dipping-needle. 


TERRESTRIAL   MAGNETISM. 


207 


the  —  pole  of  the  bar  ;  after  passing  the  middle  of  the  bar  the 
+  pole  begins  to  dip,  and  the  dip  increases  until  the  needle  reaches 
the  end  of  the  bar,  when  the  needle  is  again  vertical  with  its  +  pole 
down. 

If  the  same  needle  be  carried  northward  or  southward  along  the 
earth's  surface,  it  will  dip  in  the  same  way  as  it  approaches  the  polar 
regions,  and  be  horizontal  only  at  or  near  the  equator. 

The  experiment  presents  a  true  exhibition,  on  a  small 
scale,  of  what  the  earth  does  on  a  large  one,  and  thereby 


Fig.  174. 

presents  one  of  many  phenomena  which  lead  to  the  con- 
clusion that  the  earth  is  a  magnet.  In  other  words,  these 
phenomena  are  just  what  we  should  expect  if  a  huge 
magnet  were  thrust  through  the  earth,  as  represented  in 
Figure  174,  —  having  its  N-pole  near  the  S  geographical 
pole,  and  its  S-pole  near  the  N  geographical  pole  ;  or  if 
the  earth  itself  were  a  magnet. 


208  ENERGY  OF  ELECTRIC  FLOW. 

193.  Magnetic  Poles  of  the  Earth.  —  Points  on  the 
earth's  surface  where  the  dipping-needle  assumes  a  vertical 
position  are  called  the  magnetic  poles  of  the  earth.    A  point 
was  found  on  the  western  coast  of  Boothia,  by  Sir  James 
Ross,  in  the  year  1831,  where  the  dipping-needle  lacked 
only  one-sixtieth  of  a  degree  of  pointing  directly  to  the 
earth's  center.     The  same  voyager  subsequently  reached  a 
point  in  Victoria  Land  where  the  opposite  pole  of   the 
needle  lacked  only  1°  20 '  of  pointing  to  the  earth's  center. 

It  will  be  seen  that,  if  we  call  that  end  of  a  magnetic  needle  which 
points  north  the  N-pole,  we  must  call  that  magnetic  pole  of  the  earth 
which  is  in  the  northern  hemisphere  the  S-pole,  and  vice  versa.  (See 
Fig.  174.)  Hence,  to  avoid  confusion,  many  careful  writers  abstain  from 
the  use  of  the  terms  north  and  south  poles,  and  substitute  for  them  the 
terms  positive  and  negative,  or  marked  and  unmarked  poles. 

194.  Variation    of  the    Needle.  —  Inasmuch    as    the 
magnetic  poles   of   the   earth  do  not  coincide   with   the 
geographical  poles,  it  follows  that  the  needle  does  not  in 
most  places  point  due  north  and  south.     The  angle  which 
the  vertical  plane  through  the  axis  of  a  freely  suspended 
needle  makes  with  the  geographical  meridian  of  the  place 
is  known  as  the  angle  of  declination.     In  other  words  the 
angle  of  declination  is  the  angle  formed  by  the  magnetic 
and  geographical  meridians.    This  angle  differs  at  different 
places.     The  magnetic  axis  of  a  needle  is  a  straight  line 
connecting  its  two  poles. 

195.  Isogfonic  curves.  —  These  are  lines  connecting  all  points 
of  equal  declination  on  the  earth's  surface.     The  line  of  no  declination, 
or  isogonic  of  0°  (Fig.  175),  commences  at  the  N.  magnetic  pole  about  lat. 
70°,  long.  96°,  passes  in  a  southeasterly  direction  across  Lake  Erie  and 
Western  Pennsylvania,  and  enters  the  Atlantic  Ocean  near  the  boundary 
between  the  Carolinas.      Pursuing  its  course  through  the  south  polar 
regions,   it  reappears  in  the  eastern  hemisphere    and  crosses  Western 


MAGNETIC   RELATIONS   OF   THE   CURRENT. 


209 


Australia,  the  Caspian  Sea,  and  thence  to  the  Arctic  Ocean.  There  is 
also  a  detached  line  of  no  declination  inclosing  an  oval  area  in  Eastern 
Asia  and  the  Pacific  Ocean.  In  the  eastern  (or  Atlantic)  hemisphere, 
bounded  by  the  line  of  no  declination,  the  declination  is  westward,  as 


Fig.  175. 

indicated  by  continuous  lines  in  the  figure.     In  the  western  (or  Pacific) 
hemisphere  the  declination  is  eastward,  as  indicated  by  dotted  lines. 

The  magnetic  poles  are  not  fixed  objects  that  can  be  located  like  an 
island  or  cape,  but  are  constantly  changing.  They  appear  to  swing, 
something  like  a  pendulum,  in  an  easterly  and  westerly  direction,  each 
swing  requiring  centuries  to  complete  it.  The  north  magnetic  pole  is 
now  on  its  westerly  swing. 


Section  XI. 


MAGNETIC   RELATIONS   OF   THE   CURRENT. 

ELECTRO-MAGNETS. 

196.    Magnetic  Field  due  to  a  Circular  Current.  — 

If  a  wire  be  bent  into  the  form  of  a  circle  of  about  10  in. 
diameter,  and  placed  vertically  in  the  magnetic  meridian, 


210 


ENERGY    OF    ELECTRIC    FLOW. 


and  a  cardboard  be  placed  at  right  angles  to  the  circle  so 
that  its  horizontal  diameter  is  coincident  with  the  upper 
surface  of  the  cardboard,  and  a  very  strong  current  be 
sent  through  the  wire  in  the  direction  indicated  by  the 
arrow-head  in  the  wire,  iron  filings  sifted  upon  the  card 
will  arrange  themselves  as  shown  in  Figure  176.  And  if 
a  freely  suspended  test-needle  be  carried  inside  and  out- 


Fig.  176. 

side  the  circle,  the  several  positions  taken  by  the  needle, 
as  indicated  in  the  figure  by  arrows,  corroborate  the  direc- 
tions of  the  lines  of  force  as  indicated  by  the  filings.  If 
the  direction  of  the  current  be  reversed,  the  direction  of 
the  needle  will  be  reversed  wherever  it  may  be  placed. 

In  fact,  when  a  current  traverses  a  wire  (or  other  con- 
ductor) lines  of  force  encircle  the  electric  current  at  right 
angles  to  it.1  The  electric  current  and  its  encircling  lines 
of  force  always  coexist,  and  one  varies  directly  as  the 
other  when  there  is  no  magnetic  substance  near  the  wire. 

1"  Every  conducting  wire  is  surrounded  by  a  sort  of  magnetic  whirl.  A  great 
part  of  the  energy  of  the  so-called  electric  current  in  the  wire  consists  in  these 
external  magnetic  whirls.  To  set  them  up  requires  an  expenditure  of  energy  ;  and 
to  maintain  them  requires  a  constant  expenditure  of  energy.  It  is  these  magnetic 
whirls  which  act  on  magnets,  and  cause  them  to  set,  as  galvanometer  needles  do,  at 
right  angles  to  the  conducting  wire."  —  S.  P.  THOMPSON. 


MAGNETIC    RELATIONS    OF    THE    CURRENT. 


211 


Fig.  177. 


197.  Solenoid.  —  If  instead  of  a  single  circle  of  wire 
an  insulated  wire  be  wound  into  a  helix  of  several  turns, 
it  is  called  a  solenoid.    The  intensity  of  the  magnetic  field 
is  greatly  increased  by  the  joint  action  of  the  many  cur- 
rent turns.     The  passage  of  an  electric  current  through 
a  solenoid   gives  it  all 

the  properties  of  a  mag- 
net. The  magnetic  field 
within  the  solenoid  is 
nearly  uniform  in 
strength,  and  the  lines 
of  force  to  within  a 
short  distance  of  its  ends  are  parallel  with  its  axis,  as 
shown  in  Figure  177. 

A  solenoid  encircling  an  iron  core  constitutes  an  electro- 
magnet. 

The  iron  core  greatly  increases  the  number  of  lines  of 
force  which  pass  through  the  solenoid  by  reason  of  its 
permeability.  Hence  the  magnetic  strength  of  a  solenoid 
is  greatly  increased  by  the  presence  of  an  iron  core. 

198.  Magnetic  Polarity  of  Electro-Magnetic  Solenoid. 

—  Figure  178  represents  a  small  battery  floating  on  water.  The  leading 

wire  of  the  cell  is  wound 
into  a  horizontal  solenoid. 
Slowly  after  the  cell  is 
floated  it  will  take  a  posi- 
tion so  that  the  axis  of 
the  solenoid  will  point 
north  and  south  like  a 
magnetic  needle.  Hold 
(say)  the  S-pole  of  a  bar 
magnet  near  that  end  of 

the  solenoid  which  points  north ;  the  solenoid  is  attracted  by  the  magnet. 

Hold  the  N-pole  of  the    magnet   near   the    north-pointing  end  of  the 

solenoid;  the  magnet  repels  the  solenoid. 


Fig.   178. 


212 


BNBEGY    OF   ELECTRIC   FLOW. 


Fig.  179. 


Repeat  the  above,  using  in  place  of 
the  bar  magnet  another  current-bear- 
ing solenoid  (Fig.  179) ;  there  will  be  a 
repetition  of  the  same  phenomena  as 
obtained  with  the  bar  magnet.  Intro- 
duce a  rod  of  soft  iron  into  the  solenoid 
held  in  the  hand,  thereby  making  of  it 
an  electro-magnet;  the  only  change 
observed  is  that  the  force  of  attraction 
and  repulsion  is  greatly  increased. 

Place  the  wire  of  another  battery  over  and  parallel  with  the  coil 
(Fig.  180),  so  that  the 
two  currents  will  flow 
in  planes  at  right  an- 
gles to  each  other.  The 
coil  is  deflected  like  a 
magnetic  needle  (Fig. 
181). 

Reverse  the  direc- 
tion   of    the    current  •Fisr'  18°* 
above  and  the  deflection  is  reversed. 


Fig.  181. 


We  thus  prove  that  a  solenoid  bearing  a  current  pos- 
sesses polarity  as  if  it  were  a  magnet,  and  that  there  can 
be  produced  by  a  current-bearing  solenoid  a  magnetic  field 
of  the  same  character  as  that  produced  by  a  permanent 
magnet.  There  is  no  essential  difference  between  a  per- 
manent magnet,  a  current-bearing  solenoid,  and  an  electro- 
magnet, except  that  the  last  may  be  made  much  stronger 
than  either  of  the  others. 

199.  Given  the  Direction  of  the  Current  in  a  Sole- 
noid, to  find  the  N-  and  S-poles  of  the  Solenoid,  and 
vice  versa. 

RULE  1.  —  Place  the  palm  of  the  right  hand  against  the 
side  of  the  solenoid  so  that  the  fingers  will  point  in  the  direc- 
tion of  the  current  passing  through  the  windings  (as  shown 


ELECTRODYNAMICS. 


213 


in  Fig.  182);  the 
thumb  will  point  in 
the  direction  of  the 
N-pole  of  the  solenoid 
or  electro-magnet.1 

RULE  2.  —  Ascer- 
tain the  N-pole  of  the 
solenoid  or  electro- 
magnet with  a  mag- 
netic needle,  and  place 
the  palm  of  the  right  hand  upon  the  solenoid  so  that  the 
outstretched  thumb  points  in  the  direction  of  the  N-pole; 
the  fingers  will  point  in  the  direction  in  which  the  current 
passes  in  the  windings. 


Fig.  183. 


Section  XII. 


ELECTRODYNAMICS.  — AMPERE  S    THEORY    OF    MAGNETISM. 

2OO.    Mutual  Action  of  Currents    on  One  Another. 

—  If  we  suppose  that  a  test-needle  be  moved  up  or  down 
just  back  of  the  current-bearing  wires  (Fig.  183),  the  N- 
and  S-poles  will  take  the  positions  indicated  by  n  and  s. 
We  may  readily  predict  from  inspection  of  the  polarity 
developed,  that  if  the  wires  were  so  suspended  as  to  be 

1  The  following  suggestion  will  often  prove  of  practical  value  :  that  is  the  south 
pole  of  a  helix  where  the  current  corresponds  to  the  motion  of  the  hands  of  a  watch, 
S,  and  that  is  the  north  pole  where  the  current  is  in  the  reverse  direction,  N! 


214 


ENERGY  OF  ELECTRIC  FLOW. 


free  to  move  either  toward  or  from  each  other,  the  pair 
of  wires  in  which  the  currents  flow  parallel  to  each 
other  and  in  the  same  direction,  A,  would  attract  each 
other,  and  the  pair  of  wires  in  which  the  currents  flow  in 
opposite  directions,  B,  would  repel  each  other;  but  if  the 


ft         II 


Fig.  183. 


Fig.  184. 


currents  be  inclined  to  each  other,  as  in  Figure  184,  they 
will  tend  to  move  into  a  position  in  which  they  will  be 
parallel  and  in  the  same  direction.  That  such  actually 
takes  place  may  be  shown  by  the  following  experiments:- — 

Experiment  143. —  Figure  185  represents  a  portion  of  a  divided 
circuit.  The  lower  ends  of  the  wires  dip  about  one-sixteenth  of  an 
inch  into  mercury,  and  the  wires  are  so  suspended  that  they  are  free 
to  move  toward  or  from  each  other.  Send  a  current  of  a  battery  of 
three  or  four  Bun  sen  cells,  in  multiple  arc,  through  this  divided  cir- 
cuit. The  two  portions  of  the  current  travel  in  the  same  direction 
and  parallel  with  each  other,  and  the  two  wires  at  the  lower  extremi- 
ties move  toward  each  other,  showing  an  attraction. 

Experiment  144 Make  the  connections  (Fig.  186)  so  that  the 

current  will  go  down  one  wire  and  up  the  other.  They  repel  each 
other. 


ELECTRODYNAMICS. 


215 


Fig.  185. 


Fig.  186. 


In  the  experiment  with  the  floating  cell  and  current- 
bearing  wire  placed  over  and 
parallel  to  the  solenoid  (Fig. 
180),  a  careful  examination 
will  disclose  the  fact  that  not 
only  do  the  planes  in  which 
the  current  flows  in  the  coil 
tend  to  become  parallel  to  the 
current  above,  but  that  the 
current  in  the  upper  half  of 
the  coil,  where  the  influence 
due  to  proximity  is  greatest, 
tends  to  place  itself  so  as  to  flow  in  the  same  direction  as 
that  of  the  current  above. 

201.  Ampere's  Laws.  —  LAW  1.    Parallel  currents,  if 
in  the  same  direction,  attract  one  another ;  and  if  in  oppo- 
site directions,  they  repel  one  another. 

LAW  2.    Currents  that  are  not  parallel  tend  to  become 
parallel  and  flow  in  the  same  direction. 

202.  Ampere's   Theory   of  Magnetism.  —  This   cele- 
brated theory  briefly  stated  is  that  magnets  and  solenoid 
systems  are  fundamentally  the  same;  that  magnetism  is 
simply  electricity  in  rotation,  and  that  a  magnetic  field 
is  a  sort  of  whirlpool  of  electricity.     Not,  of  course,  that 
a  steel  magnet   contains   an   electric  current  circulating 
round  and  round  it  as  does  an  electro-magnet,  but  that 
every  molecule  of  iron,  steel,  or  other  magnetizable  sub- 
stance is  the  seat  of  a  separate  current  circulating  round 
it  continuously  and  without  resistance,  and  thus  every 
molecule  is  a  magnet. 


216 


ENERGY  OF  ELECTRIC  FLOW. 


According  to  the  theory,  in  an  unmagnetized  bar  these  currents  lie  in 
all  possible  planes,  and,  having  no  unity  of  direction,  they  neutralize  one 
another,  and  so  their  effect  as  a  system  is  zero.  But  if  a  current  of  elec- 
tricity or  a  magnet  be  brought  near,  the  effect  of  the  induction  is  to  turn 
the  currents  into  parallel  planes,  and  in  the  same  direction,  in  conformity 
to  Ampere's  Second  Law.  If  the  retentivity  be  strong  enough,  this 
parallelism  will  be  maintained  after  the  removal  of  the  inducing  cause, 
and  a  permanent  magnet  is  the  result. 

Intensity  of  magnetization  depends  on  the  degree  of  parallelism,  and 
the  latter  depends  on  the  strength  of  the  influencing  magnet.  When 
these  currents  have  become  quite  parallel,  the  body  has  received  all  the 
magnetism  that  it  is  capable  of  receiving,  and  is  said  to  be  saturated. 

The  hypothetical  currents  that  circulate  round  a  magnetic  molecule 
we  shall  call  amperian  currents,  to  distinguish  them  from  the  known 


Fig.  187. 

current  that  traverses  the  solenoid.  In  strict  accordance  with  this  theory, 
the  poles  of  the  electro-magnet  are  determined  by  the  direction  of  the 
current  in  the  helix.  The  inductive  influence  of  the  electric  current 
causes  the  amperian  currents  to  take  the  same  direction  with  itself,  as 
represented  in  Figure  187. 


Section  XIII. 

ELECTRO-MAGNETIC    INDUCTION. 

2O3.  Description  of  Apparatus.  —  A  (Fig.  188)  is  a 
short  coil  of  coarse  wire  (i.e.  the  wire  which  it  contains  is 
comparatively  short),  and  has,  of  course,  little  resistance. 
B  is  a  long  coil  of  fine  wire  having  many  turns.  Coil 


ELECTRO-MAGNETIC   INDUCTION. 


217 


A  is  in  circuit  with  two 
Bunsen  cells  in  multiple 
arc.  This  circuit  we  call 
the  primary  circuit,  the 
current  in  this  circuit 
the  primary  or  inducing 
current,  and  the  coil  the 
primary  coil.  Another 
circuit,  having  in  it  no 
battery  or  other  means  of 
generating  a  current,  con- 
tains coil  B  and  a  galvano- 
scope  with  an  astatic  needle.1  This  circuit  is  called  the 
secondary  circuit,  the  coil  the  secondary  coil,  and  the  cur- 
rents which  circulate  through  this  circuit  are  called 
secondary  or  induced  currents. 

Experiment   145.  —  Lower   the   primary   coil   quickly  into   the 
secondary  coil,  watching  at  the  same  time  the  needle  of  the  galvano- 


Fig.  188. 


Fig.  189. 

1  This  needle  consists  of  two  needles  of  about  the  same  intensity  with  their  poles 
reversed,  fixed  parallel  with  each  other.  Though  the  needles  nearly  neutralize  each 
other  and  are  therefore  little  affected  by  the  field  of  the  earth's  magnetism,  they  are 
especially  sensitive  to  the  influence  of  the  electric  current  properly  situated. 


218  ENERGY   OF   ELECTRIC    FLOW. 

scope  to  see  whether  it  moves,  and,  if  so,  in  what  direction.  Simul- 
taneously with  this  movement  there  is  a  movement  of  the  needle, 
showing  that  a  current  must  have  passed  through  the  secondary 
circuit.  Let  the  primary  coil  rest  within  the  secondary,  until  the 
needle  comes  to  rest.  After  a  few  vibrations  the  needle  settles  at 
zero,  showing  that  the  secondary  current  was  a  temporary  one.  Now, 
watching  the  needle,  quickly  pull  the  primary  coil  out ;  another 
deflection  in  the  opposite  direction  occurs,  showing  that  a  current  in 
the  opposite  direction  is  caused  by  withdrawing  the  coil. 

It  is  evident  that  in  this  case  the  current  does  not  by  its 
mere  presence  cause  an  induced  current,  but  that  a  change 
in  the  relative  positions  of  the  two  circuits,  one  of  which 
bears  a  current,  is  necessary. 

Instead  of  a  current-bearing  coil  a  bar  magnet  may  be 
introduced  into  the  secondary  coil,  and  afterwards  with- 
drawn from  it.  The  needle  is  deflected  at  each  act  as 
before. 

Experiment  146.  —  Place  the  primary  coil  within  the  secondary. 
Open  the  primary  wire  at  some  point  and  then  close  the  circuit  (Fig. 
189)  by  bringing  in  contact  the  extremities  of  the  wires.  A  deflec- 
tion is  produced.  As  soon  as  the  needle  becomes  quiet,  break  the 
circuit  by  separating  the  wires  ;  a  deflection  in  the  opposite  direction 
occurs. 

The  same  phenomena  occur  when  the  primary  current 
is  by  any  means  suddenly  strengthened  or  weakened. 

An  examination  of  the  direction  of  these  currents  enables 
us  to  state  the  facts  as  follows  :  Starting  a  current  in  a 
primary,  increasing  the  strength  of  the  primary  current, 
or  moving  the  primary  nearer  while  the  current  is  steady, 
produces  a  transitory  current  in  the  opposite  direction  in 
the  secondary.  Stopping  the  primary,  diminishing  the 
strength  of  the  primary  current,  or  moving  the  primary 


ELECTRO-MAGNETIC    INDUCTION. 


219 


away  while  the  current  is  kept  steady,  causes  a  transitory 
current  in  the  same  direction  in  the  secondary. 

It  is  evident,  therefore,  that  the  conditions  under  which 
a  current  in  the  primary  coil  can  cause  a  current  in  a 
neighboring  secondary  depend  upon  some  change  either  in 
the  strength  of  the  primary  current  or  in  the  relative  posi- 
tions of  the  primary  and  secondary  circuits. 

The  act  by  which  the  primary,  or  a  magnet,  causes  a 
current  in  a  neighboring  secondary  is  called  magneto- 
electric  induction. 

204.  Faraday's  Law  of  Induction. — If  any  conducting 
circuit  be  placed  in  the  magnetic  field,  then,  if  a  change  of 
relative  position  or  change  of  strength  of  the  primary  current 
cause  a  change  in  the  number  of  lines  of  force  passing  through 
the  secondary,  an  electro-motive  force  is  set  up  in  the  sec- 
ondary proportional  to  the  rate  at  which  the  number  of  lines 
of  force  included  by  the  sec- 
ondary is  varying. 

Consider  the  case  of  induction 
by  a  magnet.  Let  S  (Fig.  190)  be  a 
secondary  circuit  and  N  a  magnet 
projecting  a  certain  number  of 
lines  of  force  through  the  circuit. 
If  S  be  moved  nearer  to  the  mag- 
net, say  to  S',  a  much  greater 
number  of  lines  of  force  of  the 
magnet  pass  through  the  circuit 
than  when  in  its  former  position, 
owing  to  the  divergence  of  the  lines  as  they  recede  from  the  pole. 

205.  Lenz's  Law.  —  The  law  by  which  the  direction 
of  the  induced  current  is  determined  is  known  as  Lenz's 
law,  and  may  be  expressed  as  follows  :    "In  all  cases  of 


Fig.  190. 


220  ENERGY    OF    ELECTRIC    FLOW. 

induction  the  direction  of  the  induced  current  is  such  as 
to  oppose  the  motion  which  produces  it."  Thus  approach 
develops  an  opposite  current,  since  opposite  currents  resist 
approach,  while  recession  develops  a  current  of  similar 
direction,  since  similarly  directed  currents  attract  one 
another  and  thus  resist  recession. 

It  is,  then,  apparent  that  the  current  developed  in  the 
secondary  circuit  is  at  the  expense  of  mechanical  energy, 
and  that  mechanical  energy  is,  therefore,  transformed  into 
electric  energy. 

206.  Self-induction. — "  Extra  Currents." — Not  only 
does  a  current  at  starting  and  stopping  or  changing  strength 
act  on  neighboring  conductors,  generating  currents  in  them, 
but  it  acts  upon  itself  by  a  process  which  is  called  self- 
induction.     A  current  starting  or  increasing  creates  an 
oppositely  directed  current  not  only  in  its  neighbor,  but 
also  in  its  own  wire. 

Likewise  at  the  instant  a  circuit  is  broken  a  current  is 
generated  in  the  same  direction  as  the  retiring  current, 
and  this  induced  current  causes  the  spark  seen  on  break- 
ing a  circuit. 

If  a  current  pass  through  the  helix  of  an  electro-magnet,  owing  to  the 
permeability  of  the  iron  a  far  larger  number  of  lines  of  force  traverse  its 
circuit  than  if  the  core  were  removed  ;  and  hence,  at  the  stoppage  of  the 
current,  a  correspondingly  greater  impulse  operates  in  the  wire  and 
creates  a  correspondingly  more  powerful  spark.  For  a  similar  reason 
the  self-induction  is  much  greater  in  a  coil  of  wire  than  if  the  same  wire 
were  laid  out  straight. 

20 7.  Induction   Coils.  —  If  a   core   of  iron,   or,   still 
better,  a  bundle  of  wires  (A  A,  Fig.  191),  be  inserted  in 
the  primary  coil,  it  is  evident  that  it  will  be  magnetized 


ELECTRO-MAGNETIC    INDUCTION. 


221 


and  demagnetized  every  time  the  primary  is  made  and 
broken.  The  starting  and  cessation  of  amperian  currents 
in  the  core  in  the  same  direction  as  the  primary  current, 
and  simultaneously  with  the  commencement  and  ending 
of  the  primary  current,  greatly  intensifies*  the  secondary 
current.  To  save  the  trouble  of  making  and  breaking  by 


B 


Fig.  191. 


hand  the  core  is  also  utilized  in  the  -construction  of  an 
automatic  make-and-break  piece.  A  soft  iron  hammer  b 
is  connected  with  the  steel  spring  <?,  which  is  in  turn  con- 
nected with  one  of  the  terminals  of  the  primary  wire. 
The  hammer  presses  against  the  point  of  a  screw  t?,  and 
thus,  through  the  screw,  closes  the  circuit.  But  when  a 
current  passes  through  the  primary  wire,  the  core  becomes 
magnetized,  draws  the  hammer  away  from  the  screw,  and 
breaks  the  circuit.  The  circuit  broken,  the  core  loses  its 
magnetism,  and  the  hammer  springs  back  and  closes  the 


222          ENERGY  OF  ELECTRIC  FLOW. 

circuit  again.  Thus  the  spring  and  hammer  vibrate,  and 
open  and  close  the  primary  circuit  with  great  rapidity. 
An  instrument  made  on  these  principles  is  called  an 
induction  coil. 

2O8.  Ruhmkorff's  Coil.  —  This  instrument  has  the 
important  addition  to  the  parts  already  explained  of  a 
condenser,  B  B.  This  consists  of  two  sets  of  layers  of  tin- 
foil separated  by  paraffined  paper ;  the  layers  are  con- 
nected alternately  with  one  and  the  other  electrode  of  the 
battery,  as  the  figure  shows,  so  that  they  serve  as  a  sort  of 
expansion  of  the  primary  wire.  When  the  circuit  is 
broken,  the  extra  current  tends  to  jump  across  at  5,  and  to 
vaporize  the  points  of  contact,  and  to  form  with  the  vapor 
of  metal  a  bridge  that  would  prolong  the  time  of  breaking. 
But,  when  the  condenser  is  attached,  the  extra  current 
finds  an  escape  into  it  easier  than  to  jump  across  at  5,  so 
the  vaporizing  of  the  contact  is  avoided,  and  the  time  of 
breaking  being  much  shortened,  the  secondary  is  much 
more  intense. 

The  secondary  current  is,  as  we  ought  to  expect  from 
the  extreme  rapidity  with  which  the  primary,  circuit  is 
broken,  distinguished  from  the  primary,  or  galvanic  cur- 
rent, by  its  vastly  greater  E.M.F.,  or  power  to  overcome 
resistances.  A  coil  constructed  for  Mr.  Spottiswoode  of 
London  has  two  hundred  and  eighty  miles  of  wire  in  its 
secondary  coil.  With  five  Grove  cells  this  coil  gives  a 
secondary  spark  forty-two  inches  long,  and  perforates 
glass  three  inches  thick.  Many  brilliant  experiments  may 
be  performed  with  these  coils. 


DYNAMO-ELECTRIC    MACHINES.  223 


Section   XIV. 

DYNAMO-ELECTRIC   MACHINES. 

2O9.  Principles  of  the  Dynamo.  —  The  dynamo  is  a 
device  for  transforming  mechanical  energy  into  electric 
energy.  In  the  most  improved  types  of  dynamos  this  is 
done  with  a  loss  of  less  than  five  per  cent  of  the  energy. 

The  action  of  the  dynamo  depends  upon  the  principle 
that  when  lines  of  magnetic  force  are  cut  by  a  wire  a 
difference  of  potential  is  produced  in  the  wire,  and  hence 
a  current  flows  through  the  wire,  if  its  ends  be  connected 
so  as  to  form  a  closed  circuit.  This  is  illustrated  by  the 
following  experiment. 

Experiment  147.  —  Connect  a  flat  coil  of  about  two  inches  in 
diameter,  having  several  turns  of  wire,  with  a  delicate  galvanometer, 


and  rotate  the  coil  at  one  of  the  poles  of  a  strong  magnet  on  an  axis 
at  right  angles  to  the  axis  of  the  magnet  and  the  lines  of  force,  as 
illustrated  in  Figure  192. 

The  horizontal  arrow  a  indicates  the  direction  of  the 
magnetic  lines  of  force,  the  horizontal  arrow  b  the  direc- 


224  ENERGY    OF   ELECTRIC    FLOW. 

tion  of  motion  of  the  end  of  the  coil  of  wire,  and  the 
vertical  arrow  c  the  direction  of  the  current  induced  in 
the  coil  of  wire  from  the  movement  of  the  coil  across  the 
field  of  magnetic  force  in  such  a  manner  as  to  cut  lines 
of  force. 

If  the  coil  be  moved  rapidly  in  front  of  the  magnet, 
the  current  is  stronger,  and  hence  the  E.M.F.  must  be 
greater  than  if  it  be  moved  slowly. 

Also  if  the  number  of  turns  of  wire  be  increased  the 
E.M.F.  is  correspondingly  increased,  as  will  be  shown  by 
the  increased  strength  of  current. 

We  may  continue  our  experiment  still  further  by  in- 
serting a  bar  or  disk  of  soft  iron  into  the  coil  and  again 
moving  the  end  of  the  coil  through  the  field  of  force  in 
front  of  the  north  pole  of  the  magnet.  A  very  decided 
increase  in  the  strength  of  current  is  observed.  If,  fur- 
ther, another  bar  magnet  be  placed  so  that  its  south  end 
faces  the  other  end  of  the  coil,  and  the  coil  be  fixed  at  its 
center  while  its  two  ends  are  made  to  rotate  past  the  two 
poles,  more  lines  of  force  are  cut  and  greater  E.M.F.  is 
developed,  as  is  seen  from  the  increased  strength  of  cur- 
rent. A  powerful  electro-magnet  is  preferable  as  an 
inducer  to  a  permanent  magnet,  as  its  strength  or  magnetic 
density  can  be  made  much  greater. 

We  have  now  found  that  the  strength  of  current  and 
E.M.F.  depend  upon  (1)  the  rapidity  of  motion  of  the  wire 
through  the  field ;  (2)  the  number  of  turns  of  the  wire; 
and  (3)  the  number  of  lines  of  force  cut,  or  the  strength 
of  field. 


DYNAMO-ELECTBIC    MACHINES. 


225 


DIRECTION  OF  FORCB 


210.  Rule    for    Determining-    the    Direction   of  the 
Induced   Current. —  Place  the  right  hand  (Fig.  193)  so 
that  the  direction  of 

the  forefinger  coin- 
cides with  the  direc- 
tion of  the  lines  of 
force  (as  indicated 
by  a  test  needle), 
and  the  thumb  points 
in  the  direction  of  mo- 
tion of  the  part  of  the 
conductor  under  con- 

.  7  .  7  .-.  FiS>  193. 

sideration ;   the  mid- 
dle   finger    will    indicate    the    direction    of    the    induced 
current. 

211.  The  Dynamo.  —  We  are  now  prepared  to  study 
the  action  of  the  dynamo.     Our  inducing  magnet,  which 
is  commonly  an  electro-magnet,  is  called  the  field  magnet, 

and  our  coil  or  series  of  coils 
of  wire,  which  is  generally 
made  to  move  in  front  of 
the  poles  of  the  field  magnet, 
is  called  the  armature.  The 
armature  is  that  part  of  the 
electric  circuit  in  which  the 
induced  current  is  generated. 
Like  the  battery,  it  may  be 
considered  as  the  source  of 
the  current.  The  number  of 
lines  of  force  passing  through  a  circuit  may  in  general  be 
changed  in  two  ways:  either  (1)  by  moving  the  circuit 


Fig.  194. 


226 


ENERGY    OF   ELECTRIC    FLOW. 


=>v 


Fig.  195. 


through  a  field  in  which  the 

density  of  the  lines  of  force 

varies,     as    represented    in 
'    Figure  194  ;  or  (2)  by  rotat- 
ing the  plane  of  the  circuit 
—    so  as  to  change    the  angle 
which  it  makes  with  the  line 
HZ    of  force,  thus  increasing  or 
decreasing  the  number  which 
the    circuit    encloses    (Fig. 

195).  A  common  simple  form  of  dynamo  is  illustrated 
in  Figure  196.  A  large  mass  or  bar  of  soft  iron  of  the  U 
form,  surrounded 
with  a  coil  of  in- 
sulated wire,  and 
terminating  in  the 
pole  pieces  N  and 
S,  forms  the  field 
magnet.  The  ar- 
mature consists  of 
a  single  rectangu- 
lar loop  of  wire 
fixed  to  a  horizon-  Fig'  196' 

tal  axis  and  terminating  in  two  rings  of  metal,  a  and  6, 
which  are  fixed  to  the  axle,  but  insulated  from  it. 

When  a  current  passes  through  the  field  coils,  and  the 
core  becomes  magnetized,  lines  of  force  will  cross  and  fill 
the  space  between  the  pole  pieces  of  the  field  magnet. 
As  these  lines  are  cut  by  the  horizontal  parts  of  the 
rotating  wire,  an  E.M.F.  is  generated  in  these  parts,  and 
a  current  flows  in  the  direction  indicated  by  the  arrows. 


DYNAMO-ELECTRIC   MACHINES.  227 

A  metallic  or  carbon  brush  m  touches,  and  carries  off 
the  current  from,  the  lower  horizontal  segment  of  the 
rectangular  coil.  This  current  flows  through  the  external 
resistance  R,  and  completes  the  circuit  through  the  brush 
n  to  the  ring  6,  and  the  upper  half  of  the  loop.  The 
current  will  continue  to  flow  in  this  direction  while  the 
loop  moves  through  one  half  of  a  revolution.  Since 
the  lines  of  force  are  cut  in  the  opposite  direction  in  the 
next  half  revolution,  the  current  will  be  reversed  in  the 
armature  wire  and  also  through  the  external  circuit.  Thus 
with  each  half  revolution  of  the  armature  a  reversal  of 
the  current  takes  place.  This,  then,  would  be  called  an 
alternating  current  dynamo. 

212.  The  Commutator.  —  The  alternating  current  is 
not  adapted  to  all  uses,  and  for  many  purposes  it  is  desir- 
able to  have  the  current  continuously  flowing  in  the  same 
direction.  To  accomplish  this  a  commutator  is  attached  to 
the  axis  of  the  armature. 

In  Figure  197  the  two  brass  rings  a  and  6  are  replaced  by  a  single 
brass  tube  divided  into  two  parts  by  cutting  it  lengthwise.  These  two 
segments  are  attached  to  but  insulated  from  the  axis,  and  are  connected 
with  the  separate  ends  of  the 
armature  wire.  When  the 
plane  of  the  armature  coil  is 
perpendicular  to  the  line  of 
force  passing  from  N  to  S,  as 
in  Figure  197,  no  lines  of  force 
are  being  cut,  and  hence  no 
E.M.F.  is  developed  and  no 
current  flows  through  the 
loop.  But  the  instant  it  moves 
out  of  the  vertical  in  the  direc- 
tion of  the  arrow,  lines  of  force  will  be  cut,  and  as  the  lower  segment  of 
the  loop  is  moving  upward  past  the  pole  S,  and  the  other  segment  is  mov- 


228  ENERGY   OF   ELECTRIC   FLOW. 

ing  downward  in  front  of  the  pole  N,  a  positive  current  flows  from  the 
loop  through  the  segment  a,  the  brush  w?,  the  resistance  R,  the  brush  ?i, 
and  the  strip  of  the  commutator  6.  During  the  next  half  of  a  revolution 
the  lines  of  force  will  be  cut  from  an  opposite  direction  by  each  of  the 
horizontal  segments  of  the  armature  loop,  and  hence  the  current  will  be 
reversed.  But  the  segment  b  of  the  commutator  will  now  be  in  contact 
with  the  brush  m ;  and  although  the  current  is  reversed  in  the  armature  it 
will  flow  off  at  the  brush  m  as  before.  Inasmuch  as  no  E.M.F.  is 
developed  when  the  plane  of  the  loop  is  perpendicular  to  the  lines  of 
force,  it  is  at  this  point  that  the  brushes  pass  from  one  segment  to  the 
other. 

Thus  by  means  of  the  commutators  and  brushes,  reversal 
of  the  current  is  prevented  in  the  external  circuit,  although 
the  current  in  the  armature  reverses  with  each  half  revolu- 
tion. This  arrangement  will  constitute  a  direct-current 
dynamo.  We  may  have  two  turns  of  wire  before  connect- 
ing with  the  commutator  strips,  giving  twice  the  E.M.F., 
or  three  turns,  giving  three  times  the  E.M.F.  ;  i.e.  the 
E.M.F.  will  be  proportional  to  the  number  of  turns  of 
wire  in  the  coil.  Again,  instead  of  having  only  one  coil 
we  may  have  two  or  any  number  of  coils,  each  separate 
from  the  others,  and  terminating  in  strips  or  segments 
which  are  on  opposite  sides  of  the  commutator.  Generally 
the  coils  are  connected  in  series,  thus  making  any  segment 
a  terminal  of  one  coil  and  the  beginning  of  the  next. 

213.  Classes  of  Dynamos.1 —  Dynamos  may  be  divided 
into  different  classes  according  to  the  method  by  which 
their  field  magnets  are  excited.  Figure  198  illustrates  a 
magneto-electric  machine,  where  the  field  magnet  is  a  per- 
manent steel  magnet.  This  form  of  machine  is  seldom 

1  For  the  characteristics  of  the  various  classes  of  dynamos,  as  well  as  for  a  most 
lucid  and  comprehensive  treatment  of  dynamos  generally,  see  Dynamo-Electric 
Machinery,  by  S.  P.  Thompson. 


DYNAMO-ELECTKIC    MACHINES. 


229 


used,  since  a  permanent  steel  magnet  cannot  be  made  as 
powerful  as  an  electro-magnet  having  a  soft  iron  core  of 
equal  mass. 

Figure  196  illustrates  a  separately 
excited  dynamo,  where  the  field  magnet 
coils  receive  their  currents  from  a  sepa- 
rate generator,  e.g.  a  battery,  and  not 
from  the  armature  coils.  Since  an  alter- 
nating current  dynamo  does  not  produce 
a  constant  magnetic  field,  alternating 
d}^namos,  in  general,  are  separately 
excited. 


Fig.  198. 


In   a 

series 


dynamo  the  coils  of  the 
field  magnet  are  joined  in 
series  with  the  armature 
so  that  the  entire  current 
passes  through  these  coils. 

Figure  199  illustrates  a 
shunt  machine,  where  the 
field-coil  serves  as  a  shunt 
to  the  external  circuit.  L  is 
the  main  wire  and  I  is  the 
shunt  wire.  In  the  shunt 
machine  only  a  part  of  the 
current  generated  in  the 
armature  passes  through 
the  field-coils. 

A  dynamo  is  said  to  be 
"  self  -exciting  "  when  the  whole  or  any  part  (Fig.  199)  of 


Fig.  199. 


230  ENERGY   OF   ELECTRIC   FLOW. 

the  current  which  is  produced  is  used  to  magnetize  the 
field  magnets.  Such  are  the  Edison  incandescent 
dynamos. 

The  fields,  after  being  once  excited  from  any  source, 
e.g.  another  dynamo,  always  retain  a  little  residual 
magnetism,  so  that  when  the  armature  begins  to  rotate,  a 
slight  current  is  at  once  induced  in  it.  This  strengthens 
the  field,  and  the  stronger  field  reacts  to  increase  the 
current,  so  that  the  current  soon  rises  to  its  normal 
strength.  For  further  treatment  of  the  dynamo,  see 
Appendix,  Section  G. 


Section  XV. 

ELECTRIC  MOTOR. 

214.  Reversibility  of  the  Dynamo.  —  If  a  current 
from  an  external  source,  e.g.  a  battery  or  another  dynamo, 
be  passed  through  the  armature  and  field  magnet  of  a 
direct-current  dynamo,  it  will  excite  the  armature  and 
make  of  it  an  electro-magnet x  and  will  also  excite  the 
fields.  The  current  will  enter  at  the  terminals  and  will 
pass  through  the  commutator  into  the  armature.  The 
relation  of  parts  is  such  that  in  doing  this  it  will  develop 
N  and  S  poles  in  parts  of  the  periphery  of  the  armature 
distant  from  the  N  and  S  poles  of  the  fields.  Hence  there 
will  be  set  up  between  the  armature  and  the  poles  of  the 
field  magnet  a  stress  tending  to  move  the  former  a  little 


ELECTRIC    MOTOR.  231 

in  the  opposite  direction  to  that  in  which  it  is  compelled 
to  move  when  generating  a  current.  But  as  soon  as  it 
has  turned  a  short  distance,  the  action  of  the  commutator 
shifts  the  current,  and  new  poles  are  established  in  the 
armature  back  of  the  first  and  in  the  same  relative  posi- 
tions which  they  at  first  occupied.  The  armature  con- 
tinues to  rotate  as  the  new  poles  are  attracted  and  repelled, 
and  the  action  goes  on  so  long  as  a  current  is  supplied. 
Obviously  if  there  were  no  commutator  the  poles  of  the 
armature  would  be  fixed,  and  it  never  could  rotate  through 
a  greater  angle  than  180°. 

It  is  evident,  then,  that  if  two  dynamos  be  connected 
by  wires  in  the  same  circuit  and  the  armature  of  one  be 
rotated,  the  armature  of  the  other  will  rotate  in  a  reverse 
direction  as  soon  as  the  current  transmitted  from  the  first 
attains  a  certain  intensity. 

The  dynamo,  then,  is  a  reversible  machine,  in  which 
mechanical  energy  can  be  changed  directly  into  electrical 
energy  or  electrical  energy  into  mechanical  energy.  When 
the  dynamo  is  used  for  the  latter  transformation,  it  is 
commonly  known  as  an  electric  motor.  In  other  words  a 
modern  motor  is  a  dynamo  reversed.  *  The  discovery  of 
the  reversibility  of  the  dynamo  is  considered  to  be  one  of 
high  importance.  For  further  treatment  of  the  electric 
motor,  see  Appendix,  Section  H. 


232          ENERGY  OF  ELECTRIC  FLOW. 


Section  XVI. 

THE   TRANSFORMER. 

215.  The  Induction  Coil  Reversible.  —  An  induction 
coil  is  in  a  certain  sense  a  reversible  machine.  If  a  cur- 
rent of  considerable  strength  circulate  under  small  E.M.F. 
in  the  primary,  then  variations  in  its  strength  give  rise  to 
very  weak  currents  of  exceedingly  high  E.M.F.  in  the 
secondary.  Conversely,  if  we  cause  to  circulate  in  the 
secondary  weak  currents  under  very  high  E.M.F.,  by  their 
fluctuations  there  will  be  generated  in  the  primary  strong 
currents  of  small  E.M.F.  We  do  not  in  either  case  create 
electric  energy.  Electric  power  is  the  product  of  two 
factors,  current  and  electro-motive  force.  The  induction 
coil  enables  us  to  increase  one  of  these  factors  at  the 
expense  of  the  other,  and  to  transform  electric  energy  in 
form  much  as  a  mechanical  power  (e.g.  a  lever)  enables  us 
to  convert  a  quantity  of  work  which  consists  of  small 
stress  exerted  through  a  great  distance  into  a  large  stress 
exerted  through  a  small  distance. 

The  transformer  —  sometimes  called  a  converter  —  is 
merely  an  induction  coil  used  to  change  the  relation  of 
the  number  of  volts  to  the  number  of  amperes  of  any 
current.  In  a  perfect  transformer  the  number  of  watts  in 
the  primary  equals  the  number  of  watts  in  the  secondary. 

The  Ruhmkorff  coil  as  ordinarily  used  may  be  regarded 
as  a  "step  up"  transformer  from  low  potential  to  high 
potential.  But  if  the  coil  of  long  thin  wire  be  used  as  the 
primary,  it  becomes  a  "step  down  "  transformer  from  high 
potential  to  low  potential. 


THE   TRANSFORMER. 


233 


Figure  200  represents  the  coils  of  a  transformer  used  in  the  incan- 
descent lamp  service,  and  Figure  201  represents  the  same  enclosed  in  a 
case.  These  transformers  are  usually  supported  on  the  street  poles. 

The  transformer  is  applied  in  the  welding  of  metals,  i.e.  to  fuse  the 
ends  of  metals  that  are  to  be  joined  together,  where  many  hundred  or 


Fig.  2OO. 


Fig.  201. 


even  thousand  amperes  of  current,  and  only  a  fraction  of  a  volt,  would 
be  required  for  an  instant. 

A  still  wider  application  of  transformers  is  in  the  transmission  of 
electric  power.  Since  the  rate  at  which  a  current  performs  work  equals 
the  volts  times  the  amperes  (Ex  C),  then  according  to  Ohm's  law  the 
work  done  per  second  by  a  current  passing  through  a  conductor  equals 
C2R.1  That  is,  when  the  current  strength  is  doubled  there  will  be  four 
times  as  much  energy  transformed  per  second.  We  see,  then,  that  to 
transfer  electric  energy  to  a  great  distance  it  may  be  desirable  to  have  a 
high  E.M.F.  with  a  small  current  passing  through  the  mains,  and  then  to 
reduce  the  E.M.F.  and  increase  the  current  by  a  transformer  at  the  place 
where  the  energy  is  to  be  used.  By  this  means  the  expense  involved  in 
the  copper  conductors  is  much  reduced. 

For  electric  lighting  in  private  houses  transformers  are  used  to  bring 
down  the  high  potential  of  the  mains  to  the  safe  limit  of  about  100  volts. 


1  P (watts)  — Ex  C.    E=rCR  (Ohm's  formula);  by  substituting  this  value  of  E 
the  first  formula  becomes  P  =  C2R. 


234  ENERGY    OF   ELECTRIC   FLOW. 


Section  XVII. 

SECONDARY   OR    STORAGE    BATTERIES. 

216.  Reversibility  of  Electrolysis.  If  water  be 

decomposed  for  a  time  between  neutral  electrodes  such 
as  platinum  plates  and  then  the  battery  or  other  generator 
be  withdrawn  from  the  circuit  and  replaced  by  a  sensitive 
galvanometer,  a  deflection  of  the  needle  shows  that  a 
transitory  current  flows  in  the  opposite  direction  to  the 
primary  or  electrolyzing  current.  It  is  evident  that  the 
electrolyzing  current  polarizes  the  electrodes  in  the 
electrolyte,  and  that  energy  is  thus  stored  in  the  cell. 
Polarization  is  of  the  nature  of  a  counter  E.M.F.  It  is 
precisely  this  polarization  which  we  have  to  contend  with 
in  nearly  all  voltaic  cells,  and  which  we  seek  to  neutralize 
by  means  of  depolarizing  substances. 

Devices  for  thus  storing  up  energy  by  electrolysis  are 
called  storage  or  secondary  batteries,  and  sometimes  accumu- 
lators. Note  that  the  process  is  an  electrical  storage  of 
energy,  not  a  storage  of  electricity.  The  energy  of  the 
charging  current  is  transformed  into  the  potential  energy 
of  chemical  separation  in  the  storage  cell.  When  the 
circuit  of  the  storage  cell  is  closed  this  energy  is  recon- 
verted into  the  energy  of  an  electric  current  in  precisely 
the  same  way  as  with  an  ordinary  voltaic  cell. 

A  common  form  of  storage  cell  consists  of  large  lead  plates  (for 
electrodes)  covered  with  a  paste  of  red  lead  dipping  into  dilute  sulphuric 
acid.  Connected  with  a  dynamo  the  positive  electrode  becomes  by 
electrolysis  peroxydized  and  the  negative  electrode  deoxydized. 

The  storage  battery  offers  a  means  of  accumulating  energy  at  one  time 
or  place,  and  using  it  at  some  other  time  or  place.  For  example,  energy 


THERMO-ELECTRIC    CURRENTS.  235 

of  a  dynamo  current  may  be  stored  during  the  daytime  when  the  current 
is  not  needed  for  illuminating  purposes ;  and  this  energy  reconverted  into 
electric  energy  may  feed  incandescent  lamps  at  night  at  any  convenient 
place;  or  the  charged  cells  may  be  transported  to  lecture-halls,  work- 
shops, electric  cars,  etc.,  where  powerful  currents  may  be  needed. 


Section  XVIII. 

THERMO-ELECTRIC   CURRENTS. 

217.  Heat  Energy  Transformed  Directly  into  Elec- 
tric Energy. 

Experiment  148.  —  Insert  in  one  screw-cup  of  a  sensitive 
galvanometer  an  iron  wire,  and  in  the  other  cup  a  copper,  or  better, 
a  German-silver  wire.  Twist  the  other  ends  of  the  wire  together, 
and  heat  them  at  their  junction  in  a  flame;  a  deflection  of  the 
needle  shows  that  a  current  of  electricity  is  traversing  the  wire. 
Place  a  piece  of  ice  at  their  junction  ;  a  deflection  in  the  opposite 
direction  shows  that  a  current  now  traverses  the  wire  in  the  opposite 
direction. 

These  currents  are  named,  from  their  origin,  thermo- 
electric. Apparatus  required  for  the  generation  of  these 
currents  is  very  simple,  consisting  merely  of  bars  of  two 
different  metals  joined  at  one  extremity,  and  some  means 
of  raising  or  lowering  the  temperature  at  their  junction, 
or  of  raising  the  temperature  at  one  extremity  of  the  pair 
and  lowering  it  at  the  other  ;  for  the  electro-motive  force, 
and  consequently  the  strength  of  the  current,  is  nearly 
proportional  to  the  difference  in  temperature  of  the  two 
extremities  of  the  pair.  The  strength  of  the  current  is 


236  ENERGY    OF    ELECTRIC    FLOW. 

also  dependent,  as  in  the   voltaic  pair,   on  the    thermo- 
electromotive  force  of  the  metals  employed. 

218.  Thermo-Electric  Batteries.  —  A  combination  of 
the  metals  antimony  and  bismuth  makes  the  most  effective 
thermo-electric  pair.  The  E.M.F.  of  such  a  pair  is  small 
in  comparison  with  that  of  a  voltaic  pair ;  hence  the  greater 
necessity  of  combining  a  large  number  of  pairs  with  one 
another  in  series.  Such  contrivances  for  generating 
electric  currents  are  called  thermo-electric  batteries.  They 
are  seldom  used,  inasmuch  as  the  best  transform  less  than 
one  per  cent  of  the  heat  energy  employed. 


Section  XIX. 

THE    ELECTRIC    LIGHT. 

219.  Electric  Light :  Voltaic  Arc.  —  If  the  terminals 
of  wires  from  a  powerful  dynamo  or  galvanic  battery  be 
brought  together,  and  then  separated  1  or  2mm,  the 
current  does  not  cease  to  flow,  but  volatilizes  a  portion  of 
the  terminals.  The  vapor  formed  becomes  a  conductor  of 
high  resistance,  and,  remaining  at  a  very  high  temperature, 
produces  intense  light.  The  heat  is  so  great  that  it  fuses 
the  most  refractory  substances.  Metal  terminals  quickly 
melt  and  drop  off  like  tallow,  and  thereby  become  so 
far  separated  that  the  electro-motive  force  is  no  longer 
sufficient  for  the  increased  resistance,  and  the  light  is 
extinguished.  Hence,  pencils  of  carbon  (prepared  from 


THE    ELECTRIC    LIGHT. 


237 


the  coke  deposited  in  the  distillation  of  coal  inside  of  gas 
retorts),  being  less  fusible,  are  used  for  terminals. 

The  light  is  too  intense  to  admit 
of  examination  with  the  naked  eye; 
but  if  an  image  of  the  terminals  be 
thrown  on  a  screen  by  means  of  a 
lens  or  a  pin-hole  in  a  card,  an 
arch-shaped  light  is  seen  extending 
from  pole  to  pole,  as  shown  in 
Figure  202. 

The  heated  air  containing  the 
glowing  particles  of  carbon  forms 
what  is  called  the  electric  arc. 

The  larger  portion  of  the  light, 
however,  emanates  from  the  tips  of 
the  two  carbon  terminals,  which  are 
heated  to  an  intense  whiteness,  al- 
though some  emanates  from  the  arc. 
The  -f-  pole  is  hotter  than  the  - 
pole,  as  is  shown  by  its  glowing 
longer  after  the  current  is  stopped.  Flg*  303' 

The  carbon  of  the  -f-  pole  becomes  volatilized,  and  the 
light-giving  particles  are  transported  from  the  -(-  pole 
to  the  —  pole,  forming  a  bridge  of  luminous  vapor 
between  the  poles.  -What  we  see  is  not  electricity,  but 
luminous  matter. 

22O.  Electric  Lamp.  —  It  is  apparent  that  the  +  pole 
is  subject  to  a  wasting  away  ;  so  also  the  —  pole  wastes 
away,  but  not  so  fast.  At  the  point  of  the  former  a 
conical-shaped  cavity  is  formed,  while  around  the  point 
of  the  latter  warty  protuberances  appear.  When, 


238 


ENERGY    OF    ELECTRIC    FLOW. 


in  consequence  of  the  wearing  away  of 
the  -f-  pole,  the  distance  between  the  two 
pencils  becomes  too  great  for  the  electric 
current  to  span,  the  light  goes  out. 
Numerous  self-acting  regulators  for  main- 
taining a  uniform  distance  between  the 
poles  have  been  devised.  Such  an  ar- 
rangement (Fig.  203)  is  called  an  electric 
lamp.  The  movements  of  the  carbons  are 
accomplished  automatically  by  the  action 
of  the  current  itself. 

221.     Incandescent    Electric    Lamps. 

—  The  incandescent  (or  "  glow  ")  light  is 
produced  by  the  heating  of  some  refractory 
body  to  a  state  of  incandescence  by  the 
passage  of  an  electric  current.  Carbon 
filaments  are  now  al- 
most exclusively  used 
in  incandescent  lamps. 

TThe    filament    of    the 
Edison  lamp  is  carbon- 
ized bamboo.     It  is  es- 
Fig.  203.        sential  that  the  oxygen 
of  the  air  be  removed  from  these  bulbs, 
otherwise  the  carbons  would  be  quickly 
burned  out ;  hence  very  high  vacua  are 
produced  in  the  bulbs  with  a  mercury 
pump. 

Figure  204  represents  an  Edison  lamp.  The 
loop  or  filament  of  carbon,  L,  is  joined  at  n  n  to 
two  platinum  wires  which  pass  through  the  closed  end  of  the  glass  tube, 


ELECT ROT YPING  AND  ELECTROPLATING. 


239 


T.  One  of  these  wires  is  connected  with  the  brass  ring,  B,  and  the 
other  with  the  brass  button,  D,  at  the  bottom  of  the  lamp.  When  the 
lamp  is  screwed  into  its  socket,  connection  is  made  with  the  line  through 
pieces  of  brass  in  the  socket  which  are  insulated  from  each  other. 

An  Edison  16  candle-power  lamp  has  a  resistance  (when  hot)  of  about 


^Negative 


Fig.  205. 


140  ohms,  the  difference  of  potential  at  its  terminals  is  about  110  volts, 
and  it  requires  a  current  of  0.75  ampere.  Each  lamp  consumes  about 
one-tenth  of  a  horse-power. 

Incandescent  lamps  are  usually  introduced  into  the  circuit  in  multiple 
arc  (Fig.  205),  the  current  being  equally  divided  by  properly  regulating 
the  resistance  between  all  the  lamps  in  the  circuit. 


Section   XX. 


ELECTROTYPING  AND  ELECTROPLATING. 

222.  Electrotypiiig".  —  This  book  is  printed  from 
electrotype  plates.  A  molding-case  of  brass,  in  the 
shape  of  a  shallow  pan,  is  filled  to  the  depth  of  about 
one-quarter  of  an  inch  with  melted  wax.  A  few  pages 
are  set  up  in  common  type,  and  an  impression  or  mold 
is  made  by  pressing  these  into  the  wax.  The  type  is 


240 


ENERGY    OF   ELECTRIC    FLOW. 


then  distributed,  and  again  used  to  set  up  other  pages. 
Powdered  plumbago  is  applied  by  brushes  to  the  surface 
of  the  wax  mold  to  render  it  a  conductor.  The  case  is 
then  suspended  in  a  bath  of  copper  sulphate  dissolved  in 
dilute  sulphuric  acid.  The  —  pole  of  a  galvanic  battery 
or  dynamo  machine  is  applied  to  it ;  and  from  the  -f-  pole 
is  suspended  in  the  bath  a  copper  plate  opposite  and  near 
to  the  wax  face.  The  salt  of  copper  is  decomposed  by 


Fig.  306. 

the  electric  current,  and  the  copper  is  deposited  on  the 
surface  of  the  mold.  The  sulphuric  acid  appears  at  the 
-f-  pole,  and,  combining  with  the  copper  of  this  pole, 
forms  new  molecules  of  copper  sulphate.  When  the 
copper  film  has  acquired  about  the  thickness  of  an 
ordinary  visiting  card,  it  is  removed  from  the  mold.  This 
shell  shows  distinctly  every  line  of  the  types  or  engraving. 
It  is  then  backed,  or  filled  in,  with  melted  type-metal,  to 
give  firmness  to  the  plate.  The  plate  is  next  fastened  on 


THE    ELECTRIC    TELEGRAPH.  241 

a  block  of  wood,  and  thus  built  up  type-high,  and  is  now 
ready  for  the  printer.  (For  full  directions  which  will 
enable  a  pupil  to  electrotype  in  a  small  way,  see  the 
author's  Physical  Technics.) 

223.  Electroplating".  —  The  distinction  between  elec- 
troplating and  electrotyping  is  that  with  the  former  the 
metallic  coat  remains  permanently  on  the  object  on  which 
it  is  deposited,  while  with  the  latter  it  is  intended  to  be 
removed.  The  processes  are,  in  the  main,  the  same. 
The  articles  to  be  plated  are  first  thoroughly  cleaned  and 
suspended  on  the  —  pole  of  a  battery,  and  then  a  plate  of 
the  same  kind  of  metal  that  is  to  be  deposited  on  the 
given  articles  is  suspended  from  the  -f-  pole  (Fig.  206). 
The  bath  used  is  a  solution  of  a  salt  of  the  metal  to  be 
deposited.  The  cyanides  of  gold  and  silver  are  generally 
used  for  gilding  and  silvering. 


Section  XXI. 

THE   ELECTRIC   TELEGRAPH. 

224.  Morse  Telegraph.  —  First,  it  should  be  under- 
stood that,  instead  of  two  lines  of  wires  (one  to  convey 
the  electric  current  far  away  from  the  battery,  and  another 
to  return  it  to  the  battery),  if  the  distant  pole  be  connected 
with  a  large  metallic  plate  buried  in  moist  earth,  or,  still 
better,  with  a  gas  or  water  pipe  that  leads  to  the  earth, 
and  the  other  pole  near  the  battery  be  connected  in  like 
manner  with  the  earth,  so  that  the  earth  forms  about  one- 


242  ENERGY    OF    ELECTRIC    FLOW. 

half  of  the  circuit,  there  will  be  needed  only  one  wire  to 
connect  telegraphically  two  places  that  are  distant  from 
each  other. 

Let  B  (Fig.  207,  Plate  III)  represent  the  message  sender,  or  operator's 
key  ;  Y,  the  message  receiver.  It  may  be  seen  that  the  circuit  is  broken 
at  B.  Let  the  operator  press  his  finger  on  the  knob  of  the  key.  He 
closes  the  circuit,  and  the  electric  current  instantly  fills  the  wire  from 
Boston  to  New  York.  It  magnetizes  a  ;  a  draws  down  the  lever  6,  and 
presses  the  point  of  a  style  on  a  strip  of  paper,  c,  that  is  drawn  over  a 
roller.  The  operator  ceases  to  press  upon  the  key,  the  circuit  is  broken, 
and  instantly  b  is  raised  from  the  paper  by  a  spiral  spring,  d.  Let  the 
operator  press  upon  the  key  only  for  an  instant,  or  long  enough  to  count 
one  :  a  simple  dot  or  indentation  will  be  made  in  the  paper.  But  if  he 
press  upon  the  key  long  enough  to  count  three,  the  point  of  the  style  will 
remain  in  contact  with  the  paper  the  same  length  of  time  ;  and,  as  the 
paper  is  drawn  along  beneath  the  point,  a  short  straight  line  is  produced. 
This  short  line  is  called  a  dash.  These  dots  and  dashes  constitute  the 
alphabet  of  telegraphy. 

225.  The  Sounder.  —  If  the  strip  of  paper  be  removed,  and  the 
style  be  allowed  to  strike  the  metallic  roller,  a  sharp  click  is  heard. 
Again,  when  the  lever  is  drawn  up  by  the  spiral  spring  it  strikes  a  screw 
point  above  (not  represented  in  the  figure),  and  another  click,  differing 
slightly  in  sound  from  the  first,  is  heard.    A  listener  is  able  to  distinguish 
dots  from  dashes  by  the  length  of  the  intervals  of  time  that  elapse 
between  these  two  sounds.     Operators  generally  read  by  ear,  giving  heed 
to  the  clicking  sounds  produced  by  the  strokes  of  a  little  hammer.     A 
receiver  so  used  is  called  a  sounder,  a  common  form  of  which  is  repre- 
sented in  the  lower  central  part  of  Plate  III. 

226.  The  Relay.  —  The  strength  of  the  current  is  diminished,  of 
course,  as  the  line  is  extended  and  the  number  of  instruments  in  the 
circuit  is  increased.    Hence,  a  battery  that  would  give  a  current  sufficient 
to  move  the  parts  of  a  single  sounder  audibly,  on  a  short  line,  would  not 
move  the  same  parts  of  many  sounders  on  a  long  line  with  sufficient  force 
to  render  the  message  audible.     Resort  is  had  to  relays. 

In  Figure  208,  Plate  III,  R  represents  a  relay  and  S  a  sounder. 
Suppose  a  weak  current  arrives  at  New  York  from  Boston,  and  has 
sufficient  strength  to  attract  the  armature  of  the  relay  at  that  station. 
This,  as  may  be  seen  by  examination  of  the  diagram,  will  close  another 


Plate  III. 


THE   TELEPHONE.  243 

short  circuit,  called  the  local  circuit,  and  send  a  current  from  a  local 
battery  located  in  the  same  office  through  the  sounder  at  that  station. 
The  sounder,  being  operated  by  a  battery  in  a  circuit  of  only  a  few  feet 
in  length,  delivers  the  message  audibly. 


Section  XXII. 


THE   TELEPHONE. 

227.  Bell  Telephone.  —  Figure  209  represents  a  sectional  and  a 
perspective  view  of  this  instrument.  It  consists  of  a  steel  magnet,  A, 
encircled  at  one  extremity  by  a  spool  of  very  fine  insulated  wire,  B,  the 
ends  of  which  are  connected  with  the  binding  screws  D  D.  Immediately 
in  front  of  the  magnet  is  a  thin  circular  iron  disk,  E  E.  The  whole  is 
enclosed  in  a  wooden  or  rubber  case,  F.  The  conical-shaped  cavity  G 
serves  the  purpose  of  either  a  mouth-piece  or  an  ear-trumpet.  There  is 
no  difference  between  the  transmitting  and  the  receiving  telephone ;  con- 
sequently, either  instrument  may  be  employed  as  a  transmitter,  while 
the  other  serves  as  a  receiver.  Two  magneto-telephones  in  a  circuit  are 
virtually  in  the  relation  of  a  dynamo  and  a  motor.  The  transmitter 
being  in  itself  a  diminutive  dynamo,  no  battery  is  required  in  the  circuit. 
Connect  in  circuit  two  such  telephones,  and  the  apparatus  is  ready  for 
use. 

A  person  talking  near  the  disk  of  the  transmitter,  throws  it  into  rapid 
vibration.  The  disk,  being  quite  close  to  the  magnet,  is  magnetized  by 
induction  ;  and  as  it  vibrates,  its  magnetic  power  is  constantly  changing, 
being  strengthened  as  it  approaches  the  magnet,  and  enfeebled  as  it 
recedes.  This  fluctuating  magnetic  force  will  of  course  induce  currents 
in  alternate  directions  in  the  neighboring  coil  of  wire.  These  currents 
traverse  the  whole  length  of  the  wirje,  and  so  pass  through  the  coil  of  the 
distant  instrument.  When  the  direction  of  the  arriving  current  is  such 
as  to  increase  the  intensity  of  the  magnetic  field  of  the  receiver,  the 
magnet  attracts  the  iron  disk  in  front  of  it  more  strongly  than  before. 
When  the  current  is  in  the  opposite  direction,  the  disk  is  less  attracted, 
and  flies  back.  Hence  the  disk  of  the  receiving  telephone  is  forced  to 
repeat  whatever  movement  is  imparted  to  the  disk  of  the  transmitting 


244 


ENERGY    OF    ELECTRIC    FLOW. 


telephone.     The  vibrations  of  the  former  disk  become  sound  in  the  same 
manner  as  the  vibrations  of  a  tuning-fork  or  of  the  head  of  a  drum. 

The  above  is  a  description  of  the  original  and  simplest  form  of  the 
Bell  telephone.     It  is  apparent  that  the  original  energy  (i.e.  that  of  the 


Fig.  3O9. 

voice)  applied  at  the  transmitter  must,  during  its  successive  transforma- 
tions and  especially  during  its  transmission  in  the  form  of  electric  energy 
through  large  resistances,  become  very  much  enfeebled,  so  that  when  it 
reappears  as  sound,  the  sound  is  quite  feeble  and  frequently  inaudible. 


Fig.  21O. 

The  first  grand  improvement  on  the  original  consists  in  introducing  a 
battery  into  the  circuit,  and  so  arranging  that  the  voice,  instead  of  being 
obliged  to  generate  currents,  shall  be  required  only  to  render  a  current, 
already  generated  by  a  voltaic  cell,  fluctuating  or  undulating. 


THE   TELEPHONE. 


245 


The  fluctuations  are  caused  by  a  varying  resistance  in  the  circuit. 
The  pupil  must  have  learned  by  experience  ere  this  that  the  effect  of  a 
loose  contact  between  any  two  parts  of  a  circuit  is  to  increase  the 
resistance  and  thereby  weaken  the  current;  but  the  effect  of  a  slight 
variation  in  pressure  is  especially  noticeable  when  either  or  both  of  the 
parts  are  carbon.  Figure  210  illustrates  a  simple  telephonic  circuit  in 
which  are  included  a  variable  resistance  transmitter,  T,  and  a  battery,  B. 
One  of  the  electrodes,  a  platinum  point,  touches  the  center  of  the  trans- 


Fig.  313. 

mitter  disk;  the  other  electrode,  a  carbon 
button,  a,  is  pressed  by  a  spring  gently 
against  the  platinum  point.  Every  vibration 
of  the  disk,  however  minute,  causes  a  varia- 
tion in  the  pressure  between  the  two  elec- 
trodes and  a  corresponding  variation  in  the 
circuit  resistance.  As  the  resistance  changes, 
so  changes  the  current  strength,  and  thus  the 
current  is  rendered  undulatory. 

The  next  improvement  of  considerable 
importance  consists  in*  the  adoption  of  an 
induction  coil  (C,  Fig.  210),  which,  we  have 
learned,  may  produce  a  current  of  much 
greater  electro-motive  force  than  is  possessed 
by  the  original  battery  current.  Since  the 
battery  current  traverses  only  a  local  circuit, 
as  may  be  seen  by  reference  to  Figure  210,  a 
single  Leclanche"  cell  is  generally  sufficient  to 
operate  it.  The  currents  induced  by  the 
fluctuating  primary  current  traverse  the  line 

wire  and  generate  sonorous  vibrations  in  the  disk  of  the  receiver  K,  in 

the  same  manner  as  in  the  original  telephone. 

Figure  211  represents  the  entire  telephonic  apparatus  required  at  any 

single  station.     The  box  A  contains  a  small  hand-dynamo,  such  as  is 


Fig.  211. 


246 


ENERGY    OF    ELECTRIC    FLOW. 


represented  in  Figure  212.  A  person  turning  the  crank  F  generates  a 
current  which  rings  a  pair  of  electric  bells  G,  both  at  his  own  and  at  a 
distant  station,  and  thus  attracts  attention.  He  next  takes  the  receiver 
B  off  the  supporting  hook  and  places  it  at  his  ear.  When  the  weight  is 
removed  from  the  hook,  the  hook  rises  a  little  and  throws  the  dynamo 
and  bells  out  of  the  circuit,  and  at  the  same  time  introduces  the  receiver 
B,  the  transmitter  C,  and  the  battery  D,  so  that  the  circuit  stands  as 
represented  in  Figure  210.  The  box  C  contains  the  induction  coil.  E  is 
a  "lightning  arrester." 

In  Figure  212a,  A  and  B  are  buttons  of  carbon  ;  the  former  is  attached 
to  a  sounding-board  of  thin  pine  wood,  the  latter  to  a  steel  spring  C,  and 
both  are  connected  in  circuit  with  a  battery  and  a  telephone  used  as  a 
receiver.  The  spring  presses  B  against  A,  and  any  slight  jar  will  cause  a 
variation  in  the  pressure  and  corresponding  variations  in  the  current 
strength. 


A- 


Fig.  312a. 

By  means  of  this  instrument,  called  the  microphone,  any  little  sounds, 
as  its  name  indicates,  such  as  the  ticking  of  a  watch  or  the  footfall  of  an 
insect,  may  be  reproduced  at  a  considerable  distance,  and  be  as  audible 
as  though  the  original  sounds  were  made  close  to  the  ear. 


THE    TELEPHONE.  247 


REVIEW    EXERCISES. 

1.  How  is  a  body  charged  by  conduction  ?     How  by  induction  ? 

2.  In  a  circuit  of  large  resistance  which  would  be  more  sensitive, 
a  long-coil  or  a  short-coil  galvanometer  ?     Why  ? 

3.  How  does  the  condition  of  a  wire  and  its  surroundings  when 
traversed  by  a  current  differ  from  that  of  a  wire  when  not  traversed 
by  a  current  ? 

4.  What  conditions  are  prerequisite  to  a  current  of  electricity  ? 

5.  If  a  current  be  sent  through  the  armature  of  a  dynamo,  what 
happens?     Why? 

6.  Upon  what  conditions  does  the  strength  of  a  current  furnished 
by  a  dynamo  depend  ? 

7.  You  wish  to  make  an  electro-magnet  of  an  iron  rod  with  a 
certain  end  as  an  N-pole.     Explain  the  method  by  a  diagram. 

8.  What  is  the  strength  of  a  current  which  falling  15  volts  yields 
.002  horse-power  ? 

9.  When  would  you  wind  an  electro-magnet  with  fine  wire  ? 

10.  If  the  difference  of  potential  between  the  terminals  of  an  arc 
lamp  supplied  with  a  10-ampere  current  be  50  volts,  what  is  the 
power  consumed  in  the  lamp? 

11.  A  difference  of  potential  of  5.5  volts  is  maintained  at  the 
terminals  of  a  wire  of  0.1  ohm  resistance,     (a)  What  current  flows  ? 
(&)  What  is  the  power  of  the  current  ? 

12.  To  which  electrode  must  an  article  to  be  electroplated  be 
attached  ?     Why  ? 

13.  Explain,  in  accordance  with  Ampere's  theory  of  magnetism, 
the  deflection  of  a  magnetic  needle  by  an  electric  current. 

14.  What  length  of  copper  wire  .012  in.  in  diameter  will  offer  a 
resistance  of  1  ohm  ? 

15.  What  currents  are  difficult  to  insulate  ?     Why  ? 

16.  Upon  what  does  the  E.M.F.  of  a  dynamo  depend 

17.  (a)  How   does   a   storage   cell   differ  from   a   voltaic   cell? 
(6)  What  can  you  say  as  to  the  direction  of  the  current  produced 
by  each? 

18.  What  pole  of  an  electro-magnet  is  that  where  the  direction  of 
the  current  in  the  coil  is  anti-clockwise  ? 


CHAPTER   VII. 
SOUND. 

Section  I. 

STUDY   OF   VIBRATIONS   AND    WAVES. 

The  subjects  of  Sound-waves  and  Light-waves,  which  we  are  about  to 
study,  have  two  important  characteristics  in  common  that  distinguish  them 
from  the  subjects  already  studied.  First,  each  of  them  affects  its  peculiar 
organ  of  sense,  the  ear  or  the  eye.  Secondly,  both  originate  in  vibrating 
bodies,  and  reach  us  only  by  the  intervention  of  some  medium  capable 
of  being  set  in  vibration. 

228.  Period  of  Vibration. 

Experiment  149.  —  Suspend  an  iron  ball  by  a  string,  as  in  Experi- 
ment 71,  cause  it  to  vibrate,  and,  watch  in  hand,  ascertain  the  num- 
ber of  vibrations  made  in  a  given  number  of  seconds;  e.g.  60  seconds. 
Then,  remembering  that  all  the  vibrations  are  made  in  equal  intervals 
of  time,  ascertain  the  period  of  vibration  of  this  pendulum ;  i.e.  the 
time  it  takes  to  make  each  vibration,  using  the  formula 

s 

<=-> 
n 

in  which  t  =  the  period,  and  n  =  the  number  of  vibrations  made  in  s 
seconds. 

229.  Direction  of  Vibration. 

Experiment  150.  —  Grasp  one  end  of  a  small  rod  or  yardstick  in 
a  vice,  pull  the  free  end  one  side,  and  set  it  in  vibration.  Pluck  a 
string  of  a  piano  or  violin.  Note  that  the  motions  of  all  the  bodies 
which  thus  far  we  have  caused  to  vibrate  are  at  right  angles  to  their 
length.  These  are  called  transverse  vibrations. 

Experiment  151.  — Hang  up  a  spiral  spring  or  elastic  cord  with  a 
small  weight  attached  at  the  lower  end;  lift  the  weight,  and,  drop- 


STUDY   OF   VIBRATIONS    AND   WAVES.  249 

ping  it,  notice  that  the  cord  vibrates  lengthwise.  This  is  a  case  of 
Longitudinal  vibration.  There  may  also  be  torsional  vibrations,  for  ex- 
ample children  often  amuse  themselves  by  producing  these  by  twist- 
ing a  window  cord  and  tassel. 

230.  Propagation  of  Vibration ;  Waves. 

Experiment  152.  —  Take  a  rubber  cord  about  the  size  of  an  ordi- 
nary lead'pencil  and  12  feet  long.  Attach  at  intervals  a  few  glass 
beads  and  fasten  one  end  of  the  cord  to  the  wall  of  the  room.  Hold 
the  free  end  in  the  hand  and  draw  the  cord  out  so  as  to  be  nearly 
horizontal.  By  quick  movements  of  the  hand  in  a  horizontal  or  a 
vertical  direction  set  this  end  in  vibration.  Notice  that  these  vibra- 
tions are  communicated  from  point  to  point  along  the  cord,  and  that 
each  point  in  the  cord  successively  goes  through  a  vibration  precisely 
similar  to  that  held  in  the  hand.  Fix  the  eyes  upon  any  one  of  the 
beads ;  it  simply  vibrates  transversely.  Observe  the  cord  as  a  whole  ; 
waves  traverse  it  from  end  to  end,  but  it  is  easy  to  see  that  it  is  only 
a  form  that  traverses  it ;  the  beads  and  all  other  points  of  the  cord 
move  transversely.  These  successive  transverse  movements  give  rise 
to  the  wave-line  into  which  the  cord  is  thrown. 

231.  Wave-Length  and  Amplitude.  —  Imagine  an  in- 
stantaneous photograph  taken  of  the  cord  along  which  con- 
tinuous waves  are  passing.  It 

would  appear  much  like  the 

curved  line  CD  (Fig.  213).   c 

This   curved   line  represents 

what  is   known  as   a  simple 

wave-line.     The  distance  from  any  vibrating  point  to  the 

nearest  point  which  is   in  exactly  the  same  stage  of   its 

vibration  is  called  a  wave-length,  as  wx,  uv,  or  en. 

The  distance  between  the  extreme  positions  of  a  vibrat- 
ing point  or  the  length  of  its  journey  is  called  the  ampli- 
tude of  the  wave  or  the  amplitude  of  vibration. 

232.  Reflection  of  Waves ;  Interference. 
Experiment  153.  —  Stretch   the   cord  horizontally  between  two 


250 


SOUND. 


elevated  points,  and  pluck  it  with  the  hand  or  strike  it  with  a  stick 
near  one  end,  and  send  along  it  a  single  pulse,  forming  a  crest  on  the 

rope  (A,  Fig.  214).  This 
travels  to  the  other  end, 
and  there  we  see  it  re- 
flected and  inverted  (B). 
Experiment  154.  — 
Just  at  the  instant  of  re- 
flection, start  a  second 
crest ;  these  two,  the  crest 
and  the  returning  inverted 

214-  crest  or  trough  (C),  are 

now  travelling  along  the  rope  in  opposite  directions,  and  must  meet 
at  some  point.  This  point  will  be  urged  upward  by  the  crest  and 
downward  by  the  trough,  and  so  its  motion  will  be  due  to  the  differ- 
ence of  the  two  forces. 

Experiment  155.  —  Send  along  the  rope,  first  a  trough,  then  a 
crest;. now  two  crests  (D)  will  meet  near  the  middle  of  the  rope,  and 
the  motion  here  will  be  due  to  two  forces  acting  in  the  same  direc- 
tion, so  that  the  resulting  crest  will  be  greater  than  either  of  the  origi- 
nal ones. 

This  action  on  a  single  point  of  two  pulses,  or  two  trains 
of  waves,  no  matter  if  from  different  sources,  is  termed 
interference.  The  resulting  motion  may  be  greater  or  less 
than  that  due  to  either  pulse  alone,  or  it  may  be  zero. 

233.    Stationary  Vibrations,  Nodes,  etc. 

Experiment  156.  —  Hold  one  end  of  the  cord  while  the  other  is 
fixed,  and  send  along  it  a  regular  succession  of  equal  pulses  from  the 


Fig.  315. 

vibrating  hand;  it  will  be  easy,  by  varying  the  tension  and  rate  a 
little,  to  obtain  a  succession  of  hazy  spindles  (Fig.  215),  separated  by 
points  that  are  nearly  or  quite  at  rest.  Unlike  the  earlier  experiments, 


STUDY   OF    VIBRATIONS   AND    WAVES.  251 

the  waves  here  do  not  appear  to  travel  along  the  tube ;  yet  in  reality 
they  do  traverse  it.  The  deception  is  caused  by  stationary  points  being 
produced  by  the  interference  of  the  advancing  and  retreating  waves. 

This  interference  of  direct  and  reflected  waves  gives 
rise  to  the  important  class  of  so-called  stationary  vibrations. 
The  points  of  least  motion,  as  a  and  6,  are  called  nodes ; 
the  points  of  greatest  motion,  c  and  d,  are  called  antinodes  ; 
and  the  portion  of  the  rope  between  two  nodes,  as  ab^  is 
a  ventral  segment. 

234.    L/ongitudinal  Waves. 

Experiment  157.  —  Figure  216  represents  a  brass  wire  wound  in 
the  form  of  a  spiral  spring,  about  12  feet  long.  Attach  one  end  to  a 
cigar-box,  and  fasten  the  box  to  a  table.  Hold  the  other  end  H  of 
the  spiral  firmly  in  one  hand,  and  with  the  other  hand  insert  a  knife- 
blade  between  the  turns  of  the  wire,  and  quickly  rake  it  for  a  short 
distance  along  the  spiral  toward  the  box,  thereby  crowding  closer 
together  for  a  little  distance  (B)  the  turns  of  wire  in  front  of  the 
hand,  and  leaving 
the  turns  behind 
pulled  wider  apart 
(A)  for  about  an 

equal  distance.  The  Fis- 

crowded  part  of  the  spiral  may  be  called  a  condensation,  and  the 
stretched  part  a  rarefaction.  The  condensation,  followed  by  the  rare- 
faction, runs  with  great  velocity  through  the  spiral,  strikes  the 
box,  producing  a  sharp  thump ;  ic  reflected  from  the  box  to  the 
hand,  and  from  the  hand  again  to  the  box,  producing  a  second 
thump ;  and  by  skilful  manipulation  three  or  four  thumps  will  be 
produced  in  rapid  succession.  If  a  piece  of  twine  be  tied  to  some 
turn  of  the  wire,  it  will  be  seen,  as  each  wave  passes  it,  to  receive  a 
slight  jerking  movement  forward  and  backward  in  the  direction  of 
the  length  of  the  spiral. 

How  is  energy  transmitted  through  the  spring  so  as  to 
deliver  the  blow  on  the  box  ?  Certainly  not  by  a  bodily 
movement  of  the  spiral  as  a  whole,  as  might  be  the  case  if 
it  were  a  rigid  rod.  The  movement  of  the  twine  shows 


252  SOUND. 

that  the  only  motion  which  the  coil  undergoes  is  a  vibra- 
tory movement  of  its  turns.  Here,  as  in  the  case  of 
water-waves,  energy  is  transmitted  through' a  medium  by 
the  transmission  of  vibrations. 

There  are  two  important  distinctions  between  these 
waves  and  those  which  we  have  previously  studied :  the 
former  consist  of  condensations  and  rarefactions;  the 
latter,  of  elevations  and  depressions.  In  the  former,  the 
vibration  of  the  parts  is  in  the  same  line  with  the  path 
of  the  wave,  and  hence  these  are  called  longitudinal  waves  ; 
in  the  latter,  the  vibration  is  across  its  path  ;  they  are 
therefore  called  transverse  waves. 

A  wave  cannot  be  transmitted  through  an  inelastic  soft 
iron  spiral.  Elasticity  is  essential  in  a  medium,  that  it  may 
transmit  waves  composed  of  condensations  and  rarefactions  ; 
and  the  greater  the  elasticity,  the  greater  the  facility  and 
rapidity  with  which  a  medium  transmits  waves. 

235.  Air  as  a  Medium  of  Wave-Motion.  —  May  not 

air  and  other  gases,  which  are  elastic,  serve  as  media  for 
waves  ? 


Fig.  317. 

Experiment  158.  —  Place  a  candle  flame  at  the  orifice  a  of  the 
tube  (Fig.  217),  and  strike  the  table  a  sharp  blow  with  a  book  near 
the  orifice  b.  Instantly  the  candle  flame  is  quenched.  The  body  of 
air  in  the  tube  serves  as  a  medium  for  transmission  of  motion  to  the 
candle. 

Was  it  the  motion  of  a  current  of  air  through  the  tube,  a  rninia- 


STUDY   OF   VIBRATIONS  AND    WAVES.  253 

ture  wind,  or  was  it  the  transfer  of  a  vibratory  motion  ?  Burn  touch- 
paper1  at  the  orifice  b,  so  as  to  fill  this  end  of  the  tube  with  smoke, 
and  repeat  the  last  experiment. 

Evidently,  if  the  body  of  the  air  is  moved  along  through  the  tube, 
the  smoke  will  be  carried  along  with  it.  The  candle  is  blown  out  as 
before,  but  no  smoke  issues  from  the  orifice  a.  It  is  clear  that  there  is  no 
translation  of  material  particles  from  one  end  to  the  other,  —  nothing 
like  the  flight  of  a  rifle  bullet.  The  candle  flame  was  struck  by  some- 
thing like  a  pulse  of  air,  not  by  a  wind. 

236.  How  a  Wave  is  propagated  through  a  Medium. 

—  The  effect  of  applying  force  with  the  hand  to  the  spiral 
spring  is  to  produce  in  a  certain  section  (B,  Fig.  216)  of 
the  spiral  a  crowding  together  of  the  turns  of  wire,  and 
at  A  a  separation ;  but  the  elasticity  of  the  spiral  instantly 
causes  B  to  expand,  the  effect  of  which  is  to  produce  a 
crowding  together  of  the  turns  of  wire  in  front  of  it,  in 
the  section  C,  and  thus  a  forward  movement  of  the  con- 
densation is  made.  At  the  same  time,  the  expansion  of  B 
causes  a  filling  up  of  the  rarefaction  at  A,  so  that  this 
section  is  restored  to  its  normal  state.  This  is  not  all: 
the  folds  in  the  section  B  do  not  stop  in  their  swing  when 
they  have  recovered  their  original  position,  but,  like  a 
pendulum,  swing  beyond  the  position  of  rest,  thus  produc- 
ing a  rarefaction  at  B,  where  immediately  before  there 
was  a  condensation.  Thus  a  forward  movement  of  the 
rarefaction  is  made,  and  thus  a  pulse  or  wave  is  trans- 
mitted with  uniform  velocity  through  a  spiral  spring,  air, 
or  any  elastic  medium. 

237.  Graphical  Method  of  Studying  Vibrations. 
Experiment  159.  — Attach,  by  means  of  sealing-wax,  a  bristle  or 

a  fine  wire  to  the  end  of  one  of  the  prongs  of  a  large  steel  fork  (like 

1  To  prepare  touch-paper,  dissolve  about  a  teaspoonful  of  saltpetre  in  a  half-teacupful 
of  hot  water,  dip  unsized  paper  in  the  solution,  and  then  allow  it  to  dry.  The  paper 
produces  much  smoke  in  burning,  but  no  flame. 


254  SOUND. 

a  tuning-fork,  but  larger)  called  a  diapason.     Set  the  fork  in  vibra- 
tion, and  quickly  draw  the  point  of  the  bristle  lightly  over  a  smoked 

glass  (A,  Fig.  218).  A 
beautiful  wavy  line  will  be 
traced  on  the  glass,  each 

Fig.  318.  °  . 

wave    corresponding   to  a 
vibration  of  the  prong  when  vibrating  as  a  whole. 

Next,  tap  the  fork,  near  its  stem,  on  the  edge  of  a  table,  and  trace 
its  vibrations  on  a  smoked  glass  as  before.  You  will  generate  a 
similar  set  of  waves,  but,  running  over  these,  is  another  set,  of  much 
shorter  period,  like  No.  3  of  Figure  233,  showing  that  the  prong 
vibrates,  not  only  as  a  whole,  but  in  parts.  The  serrated  wavy  line 
produced  represents  the  resultant  of  the  combined  vibrations,  and 
may  be  called  a  complex  wave-line. 

QUESTIONS. 

1.  In  what  kind  of  motion  does  all  wave-motion  originate  ? 

2.  Watch  the  waves  of  the  ocean  moving  landward;  what  is  it 
that  advances? 

3.  Throw   a  cord  into  wavy  motion    by  the  movement  of  your 
hand ;  upon  what  do  the  number  and  the  length  of  the  waves  which 
traverse  the  cord  at  any  given  time  depend? 

4.  How  is  a  node  produced  ? 

5.  How  do  the  vibrations  in  longitudinal  waves  differ  from  the 
vibrations  in  transverse  waves? 

6.  Are  the  vibrations  in  air-waves  longitudinal  or  transverse? 


Section  II. 

SOUND-WAVES. 

238.  How  Sound-waves  Originate.  —  Listen  to  a 
sounding  church-bell.  It  produces  a  sensation ;  it  is 
heard.  The  ear  is  the  organ  through  which  the  sensation 


SOUND-WAVES.  255 

of  hearing  is  produced.  The  bell  is  at  such  a  distance 
that  it  cannot  act  directly  on  the  ear ;  yet  something 
must  act  on  the  ear,  and  it  must  be  the  bell  which  causes 
that  something  to  act. 

Commencing  at  the  origin  of  sound,  let  the  first  in- 
quiry be,  How  does  a  sounding  body  differ  from  a  silent 
body? 

Experiment  160.  —  Strike  a  bell  or  a  glass  bell-jar,  and  touch  the 
edge  with  a  small  cork  ball  suspended  by  a  thread ;  you  not  only  hear 
the  sound,  but,  at  the  same  time,  you  see  a  tremulous  motion  of  the 
ball,  caused  by  a  motion  of  the  bell.  Touch  the  bell  gently  with  a 
finger,  and  you  feel  a  tremulous  motion.  Press  the  hand  against  the 
bell ;  you  stop  its  vibratory  motion,  and  at  that  instant  the  sound 
ceases.  Strike  the  prongs  o'f  a  tuning-fork,  press  the  stem  against  a 
table  :  you  hear  a  sound.  Thrust,  the  ends  of  the  prongs  just  beneath 
the  surface  of  water ;  the  water  is  thrown  off  in  a  fine  spray  on  either 
side  of  the  vibrating  fork.  Watch  the  strings  of  a  piano,  guitar,  or 
violin,  or  the  tongue  of  a  jews-harp,  when  sounding.  You  can  see  that 
they  are  in  motion. 

Sound-waves  originate  in  a  vibrating  body. 

239.  How  Sound-waves  Travel.  —  How  can  a  bell, 
sounding  at  a  distance,  affect  the  ear?  If  the  bell  while 
sounding  possesses  no  peculiar  property  except  motion, 
then  it  has  nothing  to  communicate  to  th'e  ear  but  motion. 
But  motion  can  be  communicated  by  one  body  to  another 
at  a  distance  only  through  some  medium. 

Do  sound-waves  require  a  medium  for  their  communi- 
cation ? 

Experiment  161.  —  Lay  a  thick  tuft  of  cotton-wool  on  the  plate 
of  an  air-pump,  and  on  this,  face  downward,  place  a  loud-ticking 
watch,  and  cover  with  the  receiver.  Notice  that  the  receiver,  inter- 
posed between  the  watch  and  your  ear,  greatly  diminishes  the  sound, 
or  interferes  with  the  passage  of  something  to  the  ear.  Take  a  few 
strokes  of  the  pump  and  listen ;  the  sound  is  more  feeble,  and  con- 


256  SOUND. 

tinues  to  grow  less  and  less  distinct  as  the  exhaustion  progresses, 
until  either  no  sound  can  be  heard  when  the  ear  is  placed  close  to  the 
receiver,  or  an  extremely  faint  one,  as  if  coming  from  a  great  dis- 
tance. The  removal  of  air  from  a  portion  of  the  space  between  the 
watch  and  your  ear  destroys  the  sound.  Let  in  the  air  again,  and  the 
sound  is  restored. 

Sound-waves  cannot  travel  through  a  vacuum,  i.e.  with- 
out a  medium. 

Boys  often  amuse  themselves  by  inflating  paper  bags, 
and  with  a  quick  blow  bursting  them,  producing  with 
each  a  single  loud  report.  First  the  air  is  suddenly  and 
greatly  condensed  by  the  blow,  and  the  bag  is  burst ;  the 
air  now,  as  suddenly  and  with  equal  force,  expands,  and 
by  its  expansion  condenses  the  air  for  a  certain  distance 
all  around  it,  leaving  a  rarefaction  where  just  before  had 
been  a  condensation.  If  many  bags  were  burst  at  the 
same  spot  in  rapid  succession,  the  result  would  be  that 
alternating  shells  of  condensation  and  rarefaction  would 
be  thrown  off,  all  having  a  common  center,  enlarging  as 
they  advance,  like  the  waves  formed  by  stones  dropped 
into  water ;  except  that,  in  this  case,  the  waves  are  not 
like  rings,  but  hollow  globes ;  not  circular,  but  spherical. 
In  this  manner  sound-waves  produced  by  the  vibration 
of  a  sounding  body  travel  through  the  air. 

As  a  wave  advances,  each  individual  air-particle  con- 
cerned in  its  transmission  performs  a  short  excursion  to 
and  fro  in  the  direction  of  a  straight  line  radiating  from 
the  center  of  the  shells  or  hollow  globes.  A  sound-wave 
travels  its  own  length  in  the  time  that  a  particle  occupies 
in  going  through  one  complete  vibration  so  as  to  be  ready 
to  start  again. 

Experiment  162.  —  Take  a  strip  of  black  cardboard  4.5  inches  X 
1  inch.  Cut  a  slit  about  one-sixteenth  of  an  inch  wide  lengthwise 
and  centrally  through  the  strip  nearly,  from  end  to  end.  Place  the 


SOUND-WAVES. 


257 


slit  over  the  dotted  line  at  the  bottom  of  Figure  219,  and  draw  the 
book  along  underneath  in  the  direction  of  the  arrow.  Imagine  that 
the  short  white  dashes  seen  through  the  slit  represent  a  series  of  air- 
particles,  and  the  slit  itself  represents  the  direction  in  which  a  series 
of  sound-waves  are  travelling.  It  will  be  seen  that  each  air-particle 
moves  a  little  to  and  fro  in  the  direction  in  which  the  sound  travels 
and  comes  back  to  its  starting-point;  but  the  condensations  and  rare- 
factions, represented  by  a  group  (half  a  wave-length)  of  dots  being 
alternately  closer  together  or  farther  apart,  are  transmitted  through 
the  whole  series  of  air-particles. 


Fig.  219. 

240.  What  Sound  Is.  —  Sound  is  a  sensation   caused 
usually  by  waves  of  air  beating  upon  the  organ  of  hearing. 

241.  Solids  and  Liquids  as  Media  for  transmitting- 
Sound-waves. 

Experiment  163.  —  Lay  a  watch,  with  its  back  downward,  on  a 


258  SOUND. 

long  board  (or  table),  near  to  one  of  its  ends,  and  cover  the  watch 
with  loose  folds  of  cloth  till  its  ticking  cannot  be  heard  through  the 
air  in  any  direction  at  a  distance  equal  to  the  length  of  the  board. 
Now  place  the  ear  in  contact  with  the  farther  end  of  the  board,  and 
you  will  hear  the  ticking  of  the  watch  very  distinctly. 

Experiment  164.  —  Place  one  end  of  a  long  pole  on  a  cigar  box, 
and  apply  the  stem  of  a  vibrating  diapason  to  the  other  end ;  the 
sound-vibrations  will  be  transmitted  through  the  pole  to  the  box,  and 
a  loud  sound  will  be  given  out  by  the  box,  as  though  that,  and  not  the 
tuning-fork,  were  the  origin  of  the  sound. 

Experiment  165.  —  Place  the  ear  to  the  earth,  and  listen  to  the 
rumbling  of  a  distant  carriage ;  or  put  the  ear  to  one  end  of  a  long 
stick  of  timber,  and  let  some  one  gently  scratch  the  other  end  with  a 
pin. 

Solids  and  liquids,  as  well  as  gases,  transmit  sound- 
vibrations. 


Section  III. 

VELOCITY  OF   SOUND-WAVES. 

242.  The  Velocity  of  Sound-waves  tlepends  on  the 
Elasticity  and  Density  of  the  Medium.  —  The  relation 
of  velocity  to  the  density  and  elasticity  of  gases,  as  ascer- 
tained by  careful  experiment,  is  as  follows:  the  velocity 
of  sound-waves  in  gases  is  directly  proportional  to  the  square 
root  of  their  elasticity,  and  inversely  proportional  to  the 
square  root  of  their  respective  densities. 

The  velocity  of  sound-waves  in  air  at  0°  C.  is  (332.4m) 
nearly  1091  feet  per  second.  The  velocity  increases  nearly 
two  feet  for  each  degree  centigrade.  At  the  temperature 
of  16°  C.  (60°  F.)  we  may  reckon  the  velocity  of  sound- 
waves at  about  (342m)  1125  feet  per  second. 


REFLECTION   OF   SOUND-WAVES.  —  ECHOES.  259 

The  greater  density  of  solids  and  liquids,  as  compared 
with  gases,  tends,  of  coarse,  to  diminish  the  velocity  of 
sound-waves ;  but  their  greater  incompressibility  more 
than  compensates  for  the  decrease  of  velocity  occasioned 
by  the  increase  of  density.  As  a  general  rule,  solids  are 
more  incompressible  than  liquids;  hence,  sound-waves 
generally  travel  faster  in  the  former  than  in  the  latter. 
For  example,  sound-waves  travel  in  water  about  4  times 
as  fast  as  in  air,  and  in  iron  and  glass  16  times  as  fast. 


Section  IV. 

EEFLECTION  OF   SOUND-WAVES.  —  ECHOES. 

243.  Reflection. —  In  the  experiment  with  the  spiral 
spring,  waves  were  reflected  from  the  box  to  the  hand,  and 
from  the  hand  to  the  box.     When  a  sound-wave  meets  an 
obstacle  in  its  course,  it  is  reflected;    and  the  sound  re- 
sulting from  the  reflected  waves  is  often  called  an  echo, 
or,  when  they  are  many  times  reflected  sb  that  the  sound 
becomes  nearly  contin- 
uous, a  reverberation. 

244.  Sound-waves 
reflected    by   Concave 
Mirrors. 

Experiment  166. — Place 

a  watch  at  the  focus  A  (Fig.  Flg* 

220)  of  a  concave  mirror  G.  At  the  focus  B  of  another  concave 
mirror  H,  place  the  large  opening  of  a  small  tunnel,  and  with  a 
rubber  connector  attach  the  bent  glass  tube  C  to  the  nose  of  the 


260  SOUND. 

tunnel.  The  extremity  D  being  placed  in  the  ear,  the  ticking  of  the 
watch  can  be  heard  very  distinctly,  as  though  it  were  somewhere  near 
the  mirror  H.  Though  the  mirrors  be  12  feet  apart,  the  sound  will 
be  louder  at  B  than  at  an  intermediate  point  E. 

How  is  this  explained  ?  Every  air-particle  in  a  certain 
radial  line,  as  Ac,  receives  and  transmits  motion  in  the 
direction  of  this  line  ;  the  last  particle  strikes  the  mirror 
at  £,  and  being  perfectly  elastic,  bounds  off  in  the  direc- 
tion cc\  communicating  its  motion  to  the  particles  in  this 
line.  At  c'  a  similar  reflection  gives  motion  to  the  air 
particles  in  the  line  c'B.  In  consequence  of  these  two  re- 
flections, all  divergent  lines  of  motion  as  Ad,  Ae,  etc.,  that 
meet  the  mirror  G,  are  there  rendered  parallel,  and  after- 
wards rendered  convergent  at  the  mirror  H.  The  prac- 
tical result  of  the  concentration  of  this  scattering  energy 
is,  that  a  sound  of  great  intensity  is  heard  at  B.  The 
points  A  and  B  are  called  the  foci  of  the  mirrors.  The 
front  of  the  wave  as  it  leaves  A  is  convex,  in  passing 
from  G  to  H  it  is  plane,  and  from  H  to  B  concave.  If 
you  fill  a  large  circular  tin  basin  with  water,  and  strike 
one  edge  with  a  knuckle,  circular  waves  with  concave 
fronts  will  close  in  on  the  centre,  heaping  up  the  water 
at  that  point. 

Long  u  whispering-galleries  "  have  been  constructed  on  this  principle. 
Persons  stationed  at  the  foci  of  the  concave  ends  of  the  long  gallery  can 
carry  on  a  conversation  in  a  whisper  which  persons  between  cannot  hear. 

The  external  ear  is  a  wave-condenser.  The  hand  held  concave  behind 
the  ear,  by  its  increased  surface,  adds  to  its  efficiency.  An  ear-trumpet, 
by  successive  reflections,  serves  to  concentrate,  at  the  small  orifice  open- 
ing into  the  ear,  the  sound-waves  that  enter  at  the  large  end. 


INTENSITY  OF   SOUND.  261 

Section  V. 

INTENSITY  OF   SOUND. 

245.  Intensity  depends  on  the  Amplitude  of  Vibra- 
tion.—  Gently  tap  the  prongs  of  a  tuning-fork  and  dip 
them  into  water,  —  the  water  is  scarcely  moved  by  them ; 
increase  the  force  of  the  blow,  —  the  vibrations  become 
wider,  and  the  water  spray  is  thrown  with  greater  force 
and  to  a  greater  distance.  The  same  thing  occurs  when  the 
fork  vibrates  in  the  air ;  though  we  do  not  see  the  air-par- 
ticles as  they  are  batted  by  the  moving  fork,  yet  we  feel  the 
effects  as  a  sound  sensation,  and  we  judge  of  their  energy 
by  the  intensity  of  the  sensation  which  they  produce. 
Loudness  of  sound  refers  to  the  intensity  of  a  sensation. 
We  have  no  standard  of  measurement  for  a  sensation,  so 
we  are  compelled  to  measure  the  intensity  of  the  sound- 
wave, knowing  at  the  same  time  that  loudness  is  not  pro- 
portional to  this  intensity.  Unfortunately,  the  expressions 
loudness  and  intensity  of  sound-wave  are  often  inter- 
changed. The  intensity  of  a  vibration  is  measured  by 
the  energy  of  the  vibrating  particle.  It  is  clear  that  if 
the  amplitude  of  vibration  of  a  particle  is  doubled  while 
its  period  remains  constant,  its  velocity  is  doubled,  and 
its  energy  is  increased  fourfold.  Hence,  (1)  measured 
mechanically,  the  intensity  of  a  sound-wave  is  proportional 
to  the  square  of  the  amplitude  of  the  vibrations  of  the 
vibrating  body. 

246.  Intensity  depends  upon  the  Density  of  the  Me- 
dium.—  In  the  experiment  with  the  watch  under  the 
receiver  of  the  air-pump  (page  255),  the  sound  grew 


262  SOUND. 

feebler  as  the  air  became  rarer.  Aeronauts  are  obliged  to 
exert  themselves  more  to  make  their  conversation  heard 
when  they  reach  great  hights  than  when  in  the  denser 
lower  air.  (2)  The  intensity  of  sound-waves  increases  with 
the  density  of  the  medium  in  which  they  are  produced. 

247.  Intensity  depends  on   Distance.  —  It  is  a  mat- 
ter of  e very-day  observation  that  the  loudness  of  a  sound 
diminishes  very  rapidly  as  the  distance  from  the  source 
of  the  waves  to  the  ear  increases.     As  a  sound-wave  ad- 
vances  in   an   ever-widening   sphere,  a  given  amount  of 
energy  becomes  distributed  over  an  ever-increasing  sur- 
face ;  and  as  a  greater  number  of  particles  partake  of  the 
motion,  the  individual   particles   receive  proportionately 
less  energy ;  hence  it  follows,  —  as  a  consequence  of  the 
geometrical  truth,  that  "  the   surface  of  a  sphere  varies 
as  the  square  of  its  radius,"  •  -  that  (3)  the  intensity  of 
a  sound-wave  varies  inversely  as  the  square  of  the  distance 
from  its  source.     For  example,  if  two  persons,  A  and  B, 
are  respectively  500  and  1000  rods  from  a  gun  when  it 
is  discharged,  the  waves  that  reach  A  will  be  four  times 
as  intense  as  the  same  when  they  reach  B. 

248.  Speaking-Tubes. 

Experiment  167.  —  Place  a  watch  at  one  end  of  the  long  tin  tube 
(Fig.  217),  and  the  ear  at  the  other  end.  The  ticking  sounds  very 
loud,  as  though  the  watch  were  close  to  the  ear. 

Long  tin  tubes,  called  speaking-tubes,  passing  through  many  apartments 
in  a  building,  enable  persons  at  the  distant  extremities  to  carry  on  conver- 
sation in  a  low  tone  of  voice,  while  persons  in  the  various  rooms  through 
which  the  tube  passes  hear  nothing.  The  reason  is  that  the  sound-waves 
which  enter  the  tube  are  prevented  from  expanding,  consequently  the 
intensity  of  sound  is  not  affected  by  distance,  except  as  its  energy  is  wasted 
by  friction  of  the  air  against  the  sides  of  the  tube. 


REENFORCEMENT   OF  SOUND-WAVES. 


263 


Section  VI. 

REENFOKCEMENT    OF    SOUND-WAVES    AND   INTERFERENCE 
OF   SOUND-WAVES. 

249.    Reenforcement  of  Sound-waves. 

Experiment  168.  —  Set  a  diapason  in  vibration ;  you  can  scarcely 
hear  the  sound  unless  it  is  held  near  the  ear.  Press  the  stem  against 
a  table ;  the  sound  rings  out  loud,  but  the  waves  seem  to  proceed 
from  the  table. 

When  only  the  fork  vibrates,  the  prongs  presenting 
little  surface  cut  their  way  through  the  air,  producing  very 
slight  condensations,  and  consequently  waves  of  little  in- 
tensity. When  the  fork  rests  upon  the  table,  the  vibrations 
are  communicated  to  the  table ;  the  table  with  its  larger 
surface  throws  a  larger  mass  of  air  into  vibration,  and 
thus  greatly  intensifies  the  sound-waves.  The  strings  of 
the  piano,  guitar,  and  violin 
owe  as  much  of  their  loud- 
ness  of  sound  to  their  elas- 
tic sounding-boards,  as  the 
fork  does  to  the  table.  A 


25O.  Keenforcement  by 
Bodies  of  Air ;  Resona- 
tors. 

Experiment  169.  —  Take  a 
glass  tube  A  (Fig.  219),  16  inches 
long  and  2  inches  in  diameter; 
thrust  one  end  into  a  vessel  of 
water  C,  and  hold  over  the  other 
end  a  vibrating  diapason  B  that  makes  (say)  256  vibrations  in  a 
second.  Gradually  lower  the  tube  into  the  water,  and  when  it  reaches 


Fig.  331. 


264  SOUND. 

a  certain  depth,  i.e.  when  the  column  of  air  oc  attains  a  certain  length, 
the  sound  of  the  fork  becomes  very  loud;  continuing  to  lower  the 
tube,  the  sound  rapidly  dies  away. 

Columns  of  air  are  thus  found  to  serve,  as  well  as  sound- 
ing-boards, to  reenforce  sound-waves.  The  instruments 
which  enclose  the  columns  of  air  are  called  resonators. 
Unlike  sounding-boards,  they  can  respond  loudly  to  only 
one  tone,  or  to  a  few  tones  of  widely  different  pitch. 

How  is  this  reinforcement  effected  ?  When  the  prong 
a  moves  from  one  extremity  of  its  arc  a'  to  the  other  a", 
it  sends  a  condensation  down  the  tube ;  this  condensation 
striking  the  surface  of  the  water,  is  reflected  by  it  up  the 
tube.  Now  suppose  that  the  front  of  this  reflected  con- 
densation should  just  reach  the  prong  at  the  instant  it  is 
starting  on  its  retreat  from  a"  to  a' ;  then  the  reflected 
condensation  will  conspire  with  the  condensation  formed  by 
the  prong  in  its  retreat  to  make  a  greater  condensation  in 
the  air  outside  the  tube.  Again,  the  retreat  of  the  prong 
from  a'1  to  a'  produces  in  its  rear  a  rarefaction,  which  also 
runs  down  the  tube,  is  reflected,  and  will  reach  the  prong 
at  the  instant  it  is  about  to  return  from  a'  to  a",  and  to 
cause  a  rarefaction  in  its  rear;  these  two  rarefactions 
moving  in  the  same  direction  conspire  to  produce  an  in- 
tensified rarefaction.  The  original  sound-waves  thus  com- 
bine with  the  reflected,  to  produce  resonance  ;  but  this  can 
only  happen  when  the  like  parts  of  each  wave  coincide 
each  with  each ;  for  if  the  tube  were  somewhat  longer  or 
shorter  than  it  is,  it  is  plain  that  condensations  would 
meet  rarefactions  in  the  tube,  and  tend  to  destroy  one 
another. 

The  loudness  of  sound  of  all  wind  instruments  is  due  to  the  resonance 
of  the  air  contained  within  them.  A  simple  vibratory  movement  at  the 
mouth  or  orifice  of  the  instrument,  scarcely  audible  in  itself,  such  as  the 


KEENFORCEMENT   OF   SOUND-WAVES. 


265 


vibration  of  a  reed  in  reed  pipes,  or  a  pulsatory  movement  of  the  air  pro- 
duced by  the  passage  of  a  thin  sheet  of  air  over  a  sharp  wooden  or  metallic 
edge,  as  in  organ  pipes,  flutes,  and  flageolets,  or  more  simply  still  by  the 
friction  of  a  gentle  stream  of  breath  from  the  lips  sent  obliquely  across 
the  open  end  of  a  closed  tube,  bottle,  or  pen-case,  is.  sufficient  to  set  the 
large  body  of  enclosed  air  in  the  instrument  into  vibration,  and  thus  re- 
enforced,  the  sound  becomes  audible  at  long  distances. 

Experiment  170.  —  Attach  a  rose  gas-burner  A  (Fig.  222)  to  a 
metal  gas-tube  about  lm  in  length,  and  connect  this  by  a  rubber  tube 
with  a  gas-burner.  Light  the  gas  at  the  rose  burner, 
and  you  will  hear  a  low,  rustling  noise.  Remove  the 
conical  cap  from  the  long  tin  tube  (Fig.  217),  support 
the  tube  in  a  vertical  position,  and  gradually  raise  the 
burner  into  the  tube ;  when  it  reaches  a  certain  point 
not  far  up,  the  body  of  air  in  the  tube  will  catch  up 
the  vibrations,  and  give  out  deafening  sound-waves 
that  will  shake  the  walls  and  furniture  in  the  room. 


t 


251.  Measuring  Wave-Lengths  and  the 
Velocity  of  Sound-waves.  —  Experiments 
like  that  described  on  page  263  enable  us  read- 
ily to  measure  the  wave-length  produced  by  a 
fork  that  makes  a  given  number  of  vibrations 
in  a  second,  and  also  to  measure  the  velocity 
of  sound-waves.  It  is  evident  that  if  a  con-  rig.  222. 
densation  generated  by  the  prong  of  the  fork  in  which  its 
forward  movement  from  a'  to  a"  (Fig.  221)  met  with  no 
obstacle,  its  front,  meantime,  would  traverse  the  distance 
od,  or  twice  the  distance  oc ;  hence  the  length  of  the 
condensation  is  the  distance  od.  But  a  condensation  is 
only  one-half  of  a  wave,  and  the  passage  of  the  prong 
from  af  to  a"  is  only  one-half  of  a  vibration ;  conse- 
quently the  distance  od  is  one-half  of  a  wave-length,  and 
the  distance  oc  is  one-fourth  of  a  wave-length.  The 
measured  distance  of  oc  in  this  case  is  about  13.13  inches ; 
hence  the  length  of  wave  produced  by  a  C'-fork  making 


266 


SOUND. 


256  vibrations  in  a  second  is  (13.13  inches  x  4  =)  52.5 
inches  =  4.38  feet.  And  since  a  wave  from  this  fork 
travels  4.38  feet  in  ^TG  of  a  second,  it  will  travel  in  an 
entire  second  (4.38  feet  X  256  =)  1121  feet.  The  dis- 
tance oc  varies  with  the  temperature  of  the  air. 

It  is  evident  that  the  three  quantities  expressed  in  the 
formula 

velocity 


wave-length  = 


number  of  vibrations 


bear  such  a  relation  to  one  another  that  if  any  two  are 
known,  the  remaining  quantity  can  be  computed.  It 
will  further  be  observed  that  with  a  given  velocity  the  wave- 
length varies  inversely  as  the  number  of  vibrations  ;  i.e.  the 
greater  the  number  of  vibrations  per  second,  the  shorter 
the  wave-length. 

252.   Interference  of  Sound- Waves. 

Experiment  171. —  Hold  a  vibrating  diapason  over  a  resonance- 
jar  as  in  Figure  223.  Roll  the 
diapason  over  slowly  in  the  fin- 
gers. At  certain  points,  a  quarter 
of  a  revolution  apart,  when  the 
diapason  is  in  an  oblique  posi- 
tion with  reference  to  the  edge 
of  the  jar  as  represented  in  the 
figure,  the  reinforcement  from 
the  tube  almost  entirely  dis- 
appears, but  reappears  at  the 
intermediate  points.  Return  to 
the  position  where  there  is  no 
resonance,  and  enclose  in  a  loose 
roll  of  paper,  the  prong  farthest 
from  the  tube,  without  touching  the  diapason,  so  as  to  prevent  the 
sound-waves  produced  by  that  prong  from  passing  into  the  tube;  the 
resonance  resulting  from  the  vibrations  of  the  other  prong  immediately 
appears. 


Fig.  233. 


REENFORCEMENT   OF   SOUND-WAVES. 


267 


Experiment  172.  —  Select  two  of  the  tubes  (Fig.  237)  of  nearly 
the  same  length,  blow  through  them,  and  notice  the  peculiar  throbbing 
sound  produced  by  the  interference  of  the  two  sounds. 

Experiment  173.  —  Stop  one  of  the  orifices  of  a 
bicyclist's  whistle  (Fig.  224),  and  sound  one  whistle  at  a 
time.  The  sound  of  each  is  clear  and  smooth.  Sound 
both  whistles  at  the  same  time,  and  you  obtain  the  usual 
rough  and  discordant  sound. 

The  two  whistles  of  unequal  length  give  out  waves  of 
slightly  different  length,  so  that  at  certain  short  inter- 
vals the  same  phases  of  both  sets  will  coincide  (i.e.  con- 
densation with  condensation)  and  produce  intensified 
sounds  which  are  heard  at  long  distances,  while  at  other 
intervals  opposite  phases  coincide  (i.e.  condensation  with 
rarefaction),  and  the  result  of  their  mutual  destruction 
is  to  cause  the  otherwise  smooth  sound  to  become  broken 
or  rattling. 

Two  sound-ivaves  may  unite  to  produce  a  sound  louder  or 
weaker  than  either  alone  would  produce,  or  even  cause  silence. 

253.    Forced  and  Sympathetic  Vibrations. 

Experiment  174.  —  Suspend  from  a  frame  several  pendulums,  A, 

B,  C,  etc.  (Fig.  225).    A  and  D  are  each  3  feet  long,  C  a  little  longer, 
and  B  and  E  are  shorter.     Set  A  in  vibration,  and  slight  impulses 
will  be  communicated  through  the  frame  to 

D  and  cause  it  to  vibrate.  The  vibration- 
period  of  D  being  the  same  as  that  of  A, 
all  the  impulses  tend  to  accumulate  motion 
in  D,  so  that  it  soon  vibrates  through  arcs 
as  large  as  those  of  A.  On  the  other  hand, 

C,  B,  and  E,  having  different  rates  of  vibra- 
tion from  that  of  A,  will  at  first  acquire  a 
slight  motion,  but  soon  their  vibrations  will 
be  in  opposition  to  those  of  A,  and  then  the 
impulses  received  from  A  will  tend  to  destroy 
the  slight  motion  they  had  previously  acquired. 

Experiment  175. — Press  down  gently  one  of  the  keys  of  a  piano 
so  as  to  raise  the  damper  without  making  any  sound,  and  then  sing 


-268  SOUND. 

loudly  into  the  instrument  the  corresponding  note.  The  string  cor- 
responding to  this  note  will  be  thrown  into  vibrations  that  can  be 
heard  for  several  seconds  after  the  voice  ceases.  If  another  note  be 
sung,  this  string  will  respond  only  feebly. 

Raise  the  dampers  from  all  the  strings  of  the  piano  by  pressing  the 
foot  on  the  right-hand  pedal,  and  sing  strongly  some  note  into  the 
piano.  Although  all  the  strings  are  free  to  vibrate,  only  those  will 
respond  loudly  that  correspond  to  the  note  you  sing,  i.e.  those  that  are 
capable  of  making  the  same  number  of  vibrations  per  second  as  are 
produced  by  your  voice. 

These  experiments  show  that  a  vibrating  body  tends  to 
make  other  bodies  near  it  vibrate  even  if  their  periods  of 
vibrations  are  different.  Vibrations  of  this  kind,  such,  for 
example,  as  those  of  B,  C,  and  E  in  Experiment  174  and 
those  generated  in  the  sounding-boards  of  pianos,  violins, 
etc.,  are  called  forced  vibrations.  But  if  the  period  of  the 
incident  waves  of  air  is  the  same  as  that  of  the  body  which 
they  cause  to  vibrate,  the  amplitude  and  intensity  of  the 
vibrations  become  very  great,  like  that  of  the  pendulum  D, 
and  those  of  the  piano  strings  which  gave  forth  the  loud 
sounds.  Such  are  called  sympathetic  vibrations. 

QUESTIONS. 

1.  Why  do  not  sound-waves  travel  with  the  same  velocity  through 
all  bodies? 

2.  How  are  echoes  produced  ? 

3.  On  a  day  when  sound-waves  travel  through  the  air  at  the  rate  of 
1120  feet  per  second,  what  is  the  length  of  the  sound-waves  that  pro- 
ceed from  a  church  bell  which  makes  192  vibrations  in  a  second? 

4.  With  what  velocity  do  sound-waves  travel  when  a  jar  whose 
depth  is  10  inches  gives  the  maximum  reenforcement  for  a  diapason 
which  makes  256  vibrations  in  a  second? 

5.  Great   danger  often  arises  from  vibrations  of   the  walls  of  a 
building  caused  by  certain  vibratory  movements  of  machinery  within. 
The  danger  in  such  cases  can  frequently  be  greatly  diminished  by 
changing  the  rate  of  motion  in  the  machinery.     Explain. 


PITCH   OF   MUSICAL   SOUNDS. 


269 


Section  VII. 

PITCH   OF   MUSICAL   SOUNDS. 

254.  On  What  Pitch  Depends. 

Experiment  176.  —  Draw  the  finger-nail  or  a  card  slowly,  and 
then  rapidly,  across  the  teeth  of  a  comb.     The  two  sounds  produced 
are   commonly   described   as    low   or 
grave,  and  high  or  acute.     The  hight 
of  a  musical  sound  is  its  pitch. 

Experiment  177.  — Cause  the  cir- 
cular sheet-iron  disk  A  (Fig.  226)  to 
rotate,  and  hold  a  corner  of  a  visiting- 
card  so  that  at  each  hole  an  audible 
tap  shall  be  made.  Notice  that  when 
the  separate  taps  cease  to  be  distin- 
guishable, the  pitch  of  the  sound 
depends  upon  the  rapidity  of  the 
rotation,  i.e.  upon  the  frequency  of 
the  taps. 

Experiment  178.  —  Hold  the  ori- 
fice of  a  tube  B  so  as  to  blow  through 
the  holes  as  they  pass.  When  the  ear 
is  no  longer  able  to  detect  the  separate 
puffs,  the  sound  becomes  quite  musi- 
cal, and  the  pitch  rises  or  falls  with 
the  speed. 

fitch  depends  upon  the  number  of  sound-waves  striking 
the  ear  per  second,  or  upon  the  frequency  of  vibration.  The 
greater  the  number  of  vibrations  per  second,  or  the  shorter 
the  wave-length,  the  higher  is  the  pitch. 

255.  Musical  Scale.  —  Suppose  a  body,  e.g.  a  tuning  fork,  to 
make  201  vibrations  per  second,  the  sound  produced  is  recognized  by  our 


Fig.  236. 


270 


SOUND. 


musical  sense  as  the  note 


which  corresponds  with  the  so- 


called  middle  C  (c')  of  a  piano  tuned  to  the  national  standard  pitch. 

The  pitch  of  a  sound  produced  by  twice  as  many  vibrations  as  that  of 
another  sound  is  called  the  octave  of  the  latter.  Between  two  such 
sounds  the  voice  rises  or  falls,  in  a  manner  very  pleasing  to  the  ear,  by  a 
definite  number  of  steps  called  musical  intervals.  This  gives  rise  to  the 
so-called  diatonic  scale,  or  gamut. 

The  successive  tones  of  the  diatonic  scale  of  C  are  related  to  one 
another  with  respect  to  vibration  frequency  as  follows  : 


No.  of  vi- 
brations 
Ratios 

or 


256 
1 


d' 

293.62 
288    : 

9 


e' 

326.25 
320    : 


r 

348 
341.3 

I 


391.5 

:    384    : 


a 

435 
426 

f 


b'  c" 

489.37      522 

480     :     512 


Section  VIII. 

VIBRATION   OF   STRINGS. 

256.    Sonometer. 

Experiment  179.  —  Stretch  an  elastic  wire  a  over  the  bridges  of 
the  sonometer  (Fig.  228),  so  that  the  portion  between  will  be  free  to 


Fig.  228. 

vibrate.  Pluck  the  string  at  its  middle  with  the  thumb  and  finger, 
causing  it  to  vibrate,  and  observe  the  pitch.  Next  place  a  movable 
bridge  d  half-way  between  the  two  fixed  bridges  and  cause  the  portion 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSICS 


VIBRATION    OF   STRINGS. 


271 


between  either  fixed  bridge  and  the  movable  bridge  to  vibrate,  and 
observe  the  change  in  pitch.  How  is  the  vibration  period  changed? 

Experiment  180. —  Stretch  another  wire  b,  either  thicker  or  thin- 
ner than  the  last,  employing  the  same  length  and  tension  as  before, 
and  notice  the  change  in  pitch  due  to  the  difference  of  weight  of 
the  wire.  How  is  the  vibration  period  changed? 

Experiment  181.  —  Increase  the  tension  of  either  wire  by  turning 
the  pin,  to  which  one  end  of  the  wire  is  attached,  with  a  wrench  C, 
and  observe  the  change  in  pitch  caused  by  change  of  tension.  How 
does  an  increase  of  tension  affect  the  vibration  period? 

Careful  experiments  show  that  the  vibration  numbers  of 
strings  of  the  same  material  vary  inversely  as  their  lengths 
and  the' square  roots  of  their  weights,  and  directly  as  the 
square  roots  of  their  tension. 

257.   Beats. 

Experiment  182. —  Strike  simultaneously  the  lowest  note  of  a 
piano  and  its  sharp  (black  key  next  above),  and  listen  to  the  result- 
ing sound. 

You  hear  a  peculiar  wavy  or  throbbing  sound,  caused 
by  an  alternate  rising  and  sinking  in  loudness.  These 
alternations  in  loudness  are  called  beats. 


Fig.  229. 

Let  the  continuous  curve  line  AC  (Fig.  229)  represent  a 
series  of  waves  caused  by  striking  the  lower  key,  and  the 
dotted  line  a  series  of  waves  proceeding  from  the  upper 
key.  Now  the  waves  from  both  keys  may  start  together 
at  A ;  but  as  the  waves  from  the  lower  key  are  given  less 


272  SOUND. 

frequently,  so  are  they  correspondingly  longer ;  and  at 
certain  intervals,  as  at  B,  condensations  will  correspond 
with  rarefactions,  producing  by  their  interference  momen- 
tary silence,  too  short,  however,  to  be  perceived ;  but  the 
sound  as  perceived  by  the  ear  is  correctly  represented  in 
its  varying  loudness  by  the  curved  line  in  the  lower  part 
of  the  figure. 

The  number  of  heats  per  second  due  to  two  simple  tones  is 
equal  to  the  difference  of  their  respective  vibration  numbers. 
The  sensation  produced  on  the  ear  by  such  a  throbbing 
sound,  when  the  beats  are  sufficiently  frequent,  is  un- 
pleasant, much  as  the  sensation  produced  by  flashes  of 
light  that  enter  the  eye,  when  you  walk  on  the  shady 
side  of  a  picket  fence,  is  unpleasant.  The  unpleasant 
sensation,  called  by  musicians  discord,  is  due  to  beats. 


Section  IX. 

OVERTONES   AND   HARMONICS. 

258.    Vibration  in  Parts. 

Experiment  183.  —  Hang  up  a  rubber  cord  AC  (Fig.  230)  4  feet 
long,  and  fasten  both  ends.  Pluck  it  near  the  middle,  and  it  will 
swing  to  and  fro  as  a  whole  (2),  at  a  rate  dependent  on  its  length, 
tension,  etc.  Hold  it  fast  at  B  (3),  and  pluck  it  at  a  point  half-way 
between  A  and  B.  Both  halves  are  thrown  into  independent  vibra- 
tions, and  continue  so  to  vibrate  for  a  brief  time  after  the  hand  is 
withdrawn  from  B.  Again  hold  it  fast  at  B,  one-third  its  length 
above  A  (4),  and  pluck  it  half-way  between  A  and  B ;  the  length  BC 
instantly  divides  itself  at  B'  into  two  equal  parts,  and  on  withdraw- 
ing the  hand  from  B,  the  whole  cord  is  seen  to  vibrate  in  three  dis- 
tinct and  equal  sections.  In  a  similar  manner  it  may  be  made  to 
vibrate  in  four,  five,  etc.,  sections. 


OVERTONES    AND    HARMONICS.  273 

Sounds  coming  from  a  string  or  other  body  that  vibrates 
in  parts  are  called  overtones.  If,  as  is  the  case  with  a 
string,  the  vibration  num- 
ber of  the  overtone  is 
just  two,  three,  four,  etc., 
times  that  of  the  funda- 
mental or  lowest  tone, 
the  sound  is  called  a  har- 
monic. Many  overtones 
can  be  produced  from  a 
steel  bar  or  a  metallic 
plate,  but  no  harmonics. 
This  distinction  is  of 
great  importance,  for, 
practically,  no  musical 
instruments  are  of  much 
use  unless  their  vibrat- 
ing parts  furnish  harmon- 
ics- Fig.  230. 

Experiment  184.  —  Press  down  the  C'-key  (middle  C)  of  a  piano 
gently,  so  that  it  will  not  sound ;  and  while  holding  it  down,  strike 
the  C-wire  strongly.  In  a  few  seconds  release  the  key,  so  that  its 
damper  will  stop  the  vibrations  of  the  string  that  was  struck,  and 
you  will  hear  a  sound  which  you  will  recognize  by  its  pitch  as  com- 
ing from  the  C'-wire.  Place  your  finger  lightly  on  the  C'-wire,  and 
you  will  find  that  it  is  indeed  vibrating.  Press  down  the  right  pedal 
with  the  foot,  so  as  to  lift  the  dampers  from  all  the  wires,  strike  the 
C-key,  and  touch  with  the  finger  the  C'-wire ;  it  vibrates.  Touch  the 
keys  next  to  C',  viz.  B  and  Dr ;  they  have  only  a  slight  forced  vibra- 
tion. Touch  G' ;  it  vibrates. 

Now  it  is  evident  that  the  vibrations  of  the  C'  and  G'- 
wires  are  sympathetic.  A  C-wire  vibrating  as  a  whole 
cannot  cause  sympathetic  vibrations  in  a  C'-wire ;  but  if 
it  vibrates  in  halves,  it  may.  Hence  we  conclude  that 


274  SOUND. 

when  the  C-wire  was  struck,  it  vibrated,  not  only  as  a 
whole,  giving  a  sound  of  its  own  pitch,  but  also  in  halves ; 
and  the  result  of  this  latter  set  of  vibrations  was,  that  an 
additional  sound  was  produced  by  this  wire,  just  an  octave 
higher  than  the  first-mentioned  sound. 

Again,  the  G'-wire  makes  three  times  as  many  vibra- 
tions as  are  made  by  the  C-wire ;  hence  the  latter  wire, 
in  addition  to  its  vibrations  as  a  whole  and  in  halves,  must 
have  vibrated  in  thirds,  inasmuch  as  it  caused  the  G'-wire 
to  vibrate.  It  thus  appears  that  a  string  may  vibrate  at 
the  same  time  as  a  whole,  in  halves,  thirds,  etc.,  and  the 
result  is  that  a  sound  is  produced  that  is  compounded  of 
several  sounds  of  different  pitch. 

Not  only  do  stringed  instruments  produce  compound 
tones,  but  no  ordinary  musical  instrument  is  capable  of 
producing  a  simple  tone,  i.e.  a  sound  generated  by  vibra- 
tions of  a  single  period.  In  other  words,  when  any  note  of 
any  musical  instrument  is  sounded,  there  is  produced,  in 
addition  to  the  primary  tone,  a  number  of  other  tones  in  a 
progressive  series,  each  tone  of  the  series  being  usually  of 
less  intensity  than  the  preceding.  The  primary  or  lowest 
tone  of  a  note  is  usually  sufficiently  intense  to  be  the  most 
prominent,  and  hence  is  called  the  fundamental  tone. 

That  two  notes  sounded  together  may  harmonize,  it  is 
essential  not  only  that  the  pitch  of  their  fundamental  tones 
be  so  widely  different  that  they  cannot  produce  audible  beats, 
but  that  no  beat  shall  be  formed  by  their  overtones,  or  by  an 
overtone  and  a  fundamental.  Not  only  is  there  perfect 
agreement  among  the  overtones  of  two  notes  an  octave 
apart  when  sounded  together,  as  when  male  and  female 
voices  unite  in  singing  the  same  part  of  a  melody,  but 
the  richness  and  vivacity  of  the  sound  is  much  increased 
thereby. 


QUALITY   OP   SOUND.  275 

Section  X. 

QUALITY   OF   SOUND. 

259.  How  Sounds  from  Different  Sources  are  Distin- 
guished. —  We  easily  learn  to  distinguish  by  certain  pecu- 
liarities the  voices  of  our  acquaintances.     So  we  readily 
distinguish  sounds  emanating  from  various  musical  instru- 
ments, e.g.  a   piano,  violin,  harp,  and  cornet.     It  is   not 
necessarily  by  the  loudness  or  pitch  of  the  sounds  that  we 
recognize  them.    It  is  by  another  property  of  sound  called 
quality.       Two  sounds  can  differ  from  each  other  in   only 
three  particulars,  viz.  intensity,  pitch,  and  quality. 

Pitch  depends  on  frequency  of  vibrations,  loudness  on 
their  amplitude ;  on  what  does  quality  depend  ? 

260.  Analysis  of  Sounds.  —  The  unaided  ear  is  unable, 
except    to   a   very  limited 

extent,  to  distinguish  the 
individual  tones  that  com- 
pose a  note.  Helmholtz  ar- 
ranged a  series  of  resona- 
tors consisting  of  hollow 
spheres  of  brass,  each  hav- 
ing two  openings :  one  (A, 
Fig.  231)  large,  for  the  re- 
ception of  the  sound-waves,  rig.  331. 
and  the  other  (B)  small  and  funnel-shaped,  and  adapted 
for  insertion  into  the  ear.  Each  resonator  of  the  series 
was  adapted  by  its  size  to  resound  powerfully  to  only  a 
single  tone  of  a  definite  pitch.  When  any  musical  sound 
is  produced  in  front  of  these  resonators,  the  ear,  placed  at 
the  orifice  of  any  one,  is  able  to  single  out  from  a  collec- 
tion that  overtone,  if  present,  to  which  alone  this  resonator 


276 


SOUND. 


is  capable  of  responding.  In  this  manner  a  complete 
analysis  of  any  musical  sound  may  be  made,  and  the  pitch 
and  intensity  of  each  of  its  components  determined. 

It  is  found  that  when  a  note  is  produced  on  a  given  instrument,  not 
only  is  there  a  great  variety  of  intensity  represented  by  the  overtones,  but 
all  the  possible  overtones  of  the  series  are  by  no  means  present.  Which 
are  wanting  depends  very  much,  in  stringed  instruments,  upon  the  point  of 
the  string  struck.  For  example,  if  a  string  is  struck  in  its  middle,  no  node 
can  be  formed  at  that  point ;  consequently,  the  two  important  overtones 
produced  by  2  and  4  times  the  number  of  vibrations  of  the  fundamental 
will  be  wanting.  Strings  of  pianos,  violins,  etc.,  are  generally  struck  near 
one  of  their  ends,  and  thus  they  are  deprived  of  only  some  of  their  higher 
and  feebler  overtones. 

261.  Synthesis  of  Sounds.  —  The  sound  of  a  tuning- 
fork,  when  its  fundamental  is  reenforced  by  a  suitable 
resonance-cavity,  is  very  nearly  a  simple  tone.  By  sound- 
ing simultaneously  several  forks  of  different  but  appropri- 
ate pitch,  and  with  the  requisite  relative  intensities,  Helm- 
holtz  succeeded  in  producing  sounds  peculiar  to  various 
musical  instruments,  and  even  in  imitating  most  of  the 
vowel  sounds  of  the  human  voice. 


Fig.  232. 

Thus  it  appears  that  he  has  been  able  to  determine, 
both  analytically  and  synthetically,  that  the  quality  of  a 
given  sound  depends  upon  what  overtones  combine  with  its 
fundamental  tone,  and  on  their  relative  intensities;  or,  we 
may  say  more  briefly,  upon  the  form  of  vibration,  since  the 
form  must  be  determined  by  the  character  of  its  components. 


COMPOSITION   OF   SONOROUS   VIBRATIONS. 


277 


Section  XI. 

COMPOSITION  OF  SONOROUS   VIBRATIONS,    AND  THE 
RESULTANT   WAVE-FORMS. 

262.  Method  of  Representing  Sound-Vibrations 
Graphically.  —  It  is  evident  that  there  must  be  a  particular  aerial 
wave-form  corresponding  to  each  compound  vibration,  otherwise  the  ear 
would  not  be  able  to  appreciate  a  difference  in  the  quality  of  sounds  to 
which  these  combination  forms  give  rise.  Every  particle  of  air  engaged  in 


Fig.  234. 

transmitting  a  compound  sound-wave  is  simultaneously  acted  upon  by 
several  sets  of  vibratory  movements,  and  it  remains  to  investigate  what 
its  motion  will  be  under  their  joint  influence. 

The  light  wave-lines  AB  (Fig,  232)  represent  typically  two  series  of 


278 


SOUND. 


aerial  sound-waves,  corresponding  respectively  to  a  fundamental  tone  and  its 
first  overtone.  The  heavy  line  represents  the  form  of  the  joint  wave  which 
results  from  the  combination  of  the  two  constituents.  If  we  suppose  lines 
perpendicular  to  the  axis,  that  is,  to  the  dotted  line,  or  line  of  repose,  to 
be  drawn  to  each  point  in  this  line,  as  ab,  cc?,  eF,  etc.,  they  will  represent 
by  their  varying  lengths  the  displacement  of  any  particle  in  a  vibrating 
body,  or  any  particle  of  air  traversed  by  sound-waves,  from  its  normal 
position. 

The  rectangular  dia- 
gram CD  is  intended 
to  represent  a  portion 
of  a  transverse  section 
of  a  body  of  air  trav- 
ersed by  the  joint  wave 
represented  by  the 
heavy  wave-line  above. 
The  depth  of  shading 
in  different  parts  in- 
dicates the  degree  of 
condensation  at  those 
parts. 

Figure  233  repre- 
sents wave-lines  drawn 
by  an  instrument  call- 
ed a  vibrograph  (Fig. 
234).  The  second  line 
represents  a  sound  two 
octaves  above  that 
which  the  first  line  rep- 
resents, and  the  third 
line  shows  the  result  of 
the  combination  of  the 
Fig.  235.  two  sets  of  vibrations. 

263.  Manometric  Flames.  —  Apparatus  like  that  shown  in 
Figure  235  will  serve  to  illustrate  in  a  pleasing  manner  many  facts  per- 
taining to  sound  vibrations. 

The  cylindrical  box  A  is  divided  by  a  membrane  a  into  two  compart- 
ments c  and  b.  Illuminating-gas  is  introduced  into  the  compartment  c, 
through  the  rubber  tube  n,  and  burned  at  the  orifice  d.  CD  is  a  frame 
holding  two  mirrors,  M,  placed  back  to  back,  so  that  whichever  side  is 
turned  toward  the  flame  there  is  a  reflection  of  the  flame. 


COMPOSITION   OF   SONOKOUS   VIBRATIONS. 


279 


When  the  mirror  is  at  rest,  an  image  of  the  flame  will  appear  in  the 
mirror  as  represented  by  A  (Fig.  236).  If  the  mirror  is  rotated,  the 
flame  appears  drawn  out  in  a  band  of  light,  as  shown  in  B  of  the  same 
figure. 


Fig.  336. 

Sing  into  the  cone  B  (Fig.  236)  the  sound  of  oo  in  tool,  and  waves  of 
air  will  run  down  the  tube,  beat  against  the  membrane  a,  causing  it  to 
vibrate,  and  the  membrane  in  turn  acts  upon  the  gas  in  the  compartment  c, 
throwing  it  into  vibration.  The  result  is,  that  instead  of  a  flame  appear- 
ing in  the  rotating  mirror  as  a  continuous  band  of  light,  as  B,  Figure  236, 


280  SOUND. 

it  is  divided  up  into  a  series  of  tongues  of  light,  as  shown  in  C,  each  con- 
densation being  represented  by  a  tongue,  and  each  rarefaction  by  a  dark 
interval  between  the  tongues.  If  a  note  an  octave  higher  than  the  last  is 
sung,  we  obtain,  as  we  should  expect,  twice  as  many  tongues  in  the  same 
space,  as  shown  in  D.  E  represents  the  result  when  the  two  tones  are 
produced  simultaneously,  and  illustrates  in  a  striking  manner  the  effect  of 
interference.  F  represents  the  result  when  the  vowel  e  is  sung  on  the  key 
of  C' ;  and  G,  when  the  vowel  o  is  sung  on  the  same  key.  These  are  called 
manometric  flames. 


Section  XII. 

MUSICAL   INSTRUMENTS. 

264.  Classification  of  Musical  Instruments.  —  Musi- 
cal instruments  may  be  grouped  into  three  classes :  (1) 
stringed  instruments;    (2)    wind  instruments,  in  which 
the  sound  is  due  to  the  vibration  of  columns  of  air  con- 
fined  in   tubes;    (3)  instruments   in  which  the  vibrator 
is  a  membrane  or  plate.     The  first  class  has  received  its 
share  of  attention ;  the  other  two  merit  a  little  further 
consideration. 

265.  Wind  Instruments. 

Experiment  185. —  Figure  237  represents  a  set  of  Quinke's 
whistles.  The  tubes  are  of  the  same  size,  but  of  varying  length. 
Blow  through  the  small  tube  across  the  lips  of  the  large  tube  of  each 
whistle  in  the  order  of  their  lengths,  commencing  with  the  longest. 

Repeat  the  experiment,  closing  the  end  of  the  whistle  farthest 
from  you  with  a  finger,  so  as  to  make  what  is  called  a  "  closed  pipe." 

The  pitch  of  vibrating  air-columns,  as  well  as  of  strings, 
varies  with  the  length,  and  in  both  stopped  and  open  pipes 


MUSICAL  INSTRUMENTS. 


281 


the  number  of  vibrations  is  inversely  proportional  to  the 
length  of  the  pipe.  An  open  pipe  gives  a  note  an  octave 
higher  than  a  closed  pipe  of  the  same  length. 


Fig.  237. 

Experiment  186.  —  Take  some  of  the  longer  whistles,  blow  as 
before,  gradually  increasing  the  force  of  the  current.  It  will  be  found 
that  only  the  gentle  current  will  give  the  full  musical  fundamental 
tone  of  the  tube,  —  a  little  stronger  current  produces  a  mere  rustling 
sound ;  but  when  the  force  of  the  current  reaches  a  certain  limit,  an 
overtone  will  break  forth ;  and,  on  increasing  still  further  the  power 
of  the  current,  a  still  higher  overtone  may  be  reached. 

Figure  238  represents  an  open  organ-pipe  provided  with  a  glass 
window  A  in  one  of  its  sides.  A  wire  hoop  B  has  stretched  over  it  a 
membrane,  and  the  whole  is  suspended  by  a  thread  within  the  pipe.  If 
the  membrane  is  placed  near  the  upper  end,  a  buzzing  sound  proceeds 


282 


SOUND. 


from  the  membrane  when  the  fundamental  tone  of  the  pipe  is  sounded ; 
and  sand  placed  on  the  membrane  will  dance  up  and  down  in  a  lively 
manner.  On  lowering  the  membrane,  the  buzzing  sound  becomes 
fainter,  till,  at  the  middle  of  the  tube,  it  ceases  entirely,  and  the  sand 
becomes  quiet.  Lowering  the  membrane  still  further,  the  sound  and 
dancing  recommence,  and  increase  as  the  lower  end  is  approached. 

When  the  fundamental  tone  of  an  open  pipe  is  produced, 
its  air-column  divides  itself  into  two  equal  vibrating  sections, 
with  the   anti-node   at  the  extremities   of  the 
tube,  and  a  node  in  the  center. 


Fig.  338.  Fig.  239. 

If  the  pipe  is  stopped,  there  is  a  node  at  the  stopped 
end ;  if  it  is  open,  there  is  an  anti-node  at  the  open 
end;  and  in  both  cases  there  is  an  anti-node  at  the  end 
where  the  wind  enters,  which  is  always  to  a  certain 
extent  open. 

A,  B,  and  C  of  Figure  239  show  respectively  the  posi- 
tions of  the  nodes  and  anti-nodes  for  the  fundamental  tone 


MUSICAL  INSTRUMENTS. 


283 


and  first  and  second  overtones  of  a  closed  pipe ;  and 
A',  B',  and  C'  show  the  positions  of  the  same  in  an 
open  pipe  of  the  same  length.  The  distance  between  the 
dotted  lines  shows  the  relative  amplitudes  of  the  vibra- 
tions of  the  air-particles  at  various  points  along  the  tube. 
Now  the  distance  between  a  node  and  the  nearest  anti° 
node  is  a  quarter  of  a  wave-length.  Comparing,  then, 
A  and  A',  it  will  be  seen  that  the  wave-length  of  the 
fundamental  of  the  closed  pipe  must  be  twice  the  wave- 
length of  the  fundamental  of  the  open  pipe ;  hence  the 
vibration  period  of  the  latter  is  half  that  of  the  former; 
consequently  the  fundamental  of  the  open  pipe  must  be 
an  octave  higher  than  that  of  the  closed  pipe. 


Fig.  240. 

266.   Sounding  Plates,  etc. 

Experiment  187.  —  Fasten  with  a  screw  the  elastic  brass  plate  A 
(Fig.  240)  on  the  upright  support.  Strew  writing-sand  over  the  plate, 
and  draw  a  rosined  bass  bow  steadily  and  firmly  over  one  of  its 
edges  near  a  corner ;  and  at  the  same  time  touch  the  middle  of  one 


284 


SOUND. 


of  its  edges  with  the  tip  of  the  finger;  a  musical  sound  will  be 
produced,  and  the  sand  will  dance  up  and  down,  and  quickly  collect 
in  two  rows,  extending  across  the  plate  at  right  angles  to  one  an- 
other. Draw  the  bow  across  the  middle  of  an  edge,  and  touch  with  a 
finger  one  of  its  corners ;  the  sand  will  arrange  itself  in  two  diagonal 
rows  (2)  across  the  plate,  and  the  pitch  of  the  note  will  be  a  fifth 
higher.  Touch,  with  the  nails  of  the  thumb  and  forefinger,  two 
points  a  and  b  (3)  on  one  edge,  and  draw  the  bow  across  the  middle 
c  of  the  opposite  edge,  and  you  will  obtain  additional  rows  and  a 
shriller  note. 


r!"\ulun*Tr«ii-MjrrimiL'"-' 


*,Ti-v«-«w>»*i''v.v««jrMO«. 


Fig.  341. 

By  varying  the  position  of  the  point  touched  and  bowed, 
a  great  variety  of  patterns  can  be  obtained,  some  of  which 
are  represented  in  Figure  241.  It  will  be  seen  that  the 
effect  of  touching  the  plate  with  a  finger  is  to  prevent 
vibration  at  that  point,  and  consequently  a  node  is  there 
produced.  The  whole  plate  then  divides  itself  up  into 
segments  with  nodal  division  lines  in  conformity  with  the 


MUSICAL   INSTBTJMENTS.  285 

node  just  formed.  The  sand  rolls  away  from  those  parts 
which  are  alternately  thrown  into  crests  and  troughs,  to 
the  parts  that  are  at  rest. 

267.    Interference. 

Experiment  188. —  C  (Fig.  240)  is  a  tin  tube  made  in  two  parts  to 
telescope  one  within  the  other.  The  extremity  of  one  of  the  parts  ter- 
minates in  two  slightly  smaller  branches.  Bow  the  plate,  as  in  the  first 
experiment  (1),  place  the  two  orifices  of  the  branches  over  the  segments 
marked  with  the  +  signs,  and  regulate  the  length  of  the  tube  so  as  to 
reenforce  the  note  given  by  the  plate,  and  set  the  plate  in  vibration. 
Now  turn  the  tube  around,  so  that  one  orifice  may  be  over  a  +  seg- 
ment, and  the  other  over  a  —  segment ;  the  sound  due  to  resonance 
entirely  ceases.  It  thus  appears  that  the  two  segments  marked  + 
pass  through  the  same  phases  together ;  likewise  the  phases  of  —  seg- 
ments correspond  with  one  another ;  i.e.  when  one  +  segment  is 
bent  upward,  the  other  is  bent  upward,  and  at  the  same  time  the  two 
—  segments  are  bent  downward;  for,  when  the  two  orifices  of  the 
tube  are  placed  over  two  +  segments  or  two  —  segments,  two  condensa- 
tions followed  by  two  rarefactions  pass  up  these  branches  and  unite 
at  their  junction  to  produce  a  loud  sound ;  but  when  one  of  the 
orifices  is  over  a  +  segment,  and  the  other  over  a  —  segment,  a  con- 
densation passes  up  one  branch  at  the  same  time  that  a  rarefaction 
passes  up  the  other,  and  the  two  destroy  one  another  when  they  corne 
together;  i.e.  the  two  sound-waves  combine  to  produce  silence. 

268.  Bells.  —  A  bell  or  goblet  is  sub- 
ject to  the  same  laws  of  vibration  as  a 
plate. 

Experiment  189.  —  Nearly  fill  a  large  goblet 
with  water,  strew  upon  the  surface  lycopodium 
powder,  and  draw  a  rosined  bow  gently  across  the 
edge  of  the  glass.  The  surface  of  the  water  will 
become  rippled  with  wavelets  (Fig.  242)  radiating 
from  four  points  90°  apart,  corresponding  to  the 
centers  of  four  ventral  segments  into  which  the  Fig' 

goblet  is  divided,  and  the  powder  will  collect  in  lines  proceeding  from 
the  nodal  points  of  the  bell.  By  touching  the  proper  points  of  a 


286 


SOUND. 


bell  or  glass  with  a  finger-nail,  it  may  be  made  to  divide  itself,  like  a 
plate,  into  6,  8,  10,  etc.  (always  an  even  number),  vibrating  parts. 

Experiment  190.  —  Remove  the  brass  plate  (Fig.  240)  from  its 
support,  and  fasten  the  bell  B  (Fig.  243)  on  the  support.     Bow  the 

edge  of  the  bell  at  some  point,  and 
hold  the  open  tube  C  in  a  horizon- 
tal position  with  the  center  of  one 
of  its  walls  near  that  point  of  the 
edge  of  the  bell  which  is  opposite 
the  point  bowed.  The  tube  loudly 
reenforces  the  sound  of  the  bell. 
Move  the  tube  around  the  edge  of 


Fig.  243. 


the  bell  and  find  its  nodes. 


Thrust  the  plunger  D  into  the  open  end  E  of  the  tube,  and  find 
what  part  of  the  length  of  an  open  tube  a  closed  tube  should  be  to 
reenforce  a  sound  of  a  given  pitch. 

269.  Vocal  Organs.  —  It  is  difficult  to  say  which  is 
more  to  be  admired, — the  wonderful  capabilities  of  the 
human  voice  or  the  extreme  sim- 
plicity of  the  means  by  which  it  is 
produced.  The  organ  of  the  voice 
is  a  reed  instrument  situated  at  the 
top  of  the  windpipe,  or  trachea.  A 
pair  of  elastic  bands  aa  (Fig.  244), 
called  the  vocal  chords,  is  stretched 
across  the  top  of  the  windpipe.  The 
air-passage  6,  between  these  chords, 
is  open  while  a  person  is  breathing ; 
Fig.  344.  k^  wnen  he  speaks  or  sings,  they 

are  brought  together  so  as  to  form  a  narrow,  slit-like 
opening,  thus  making  a  sort  of  double  reed,  which  vibrates 
when  air  is  forced  from  the  lungs  through  the  narrow 
passage,  somewhat  like  the  little  tongue  of  a  toy  trum- 
pet. The  sounds  are  grave  or  high  according  to  the 
tension  of  the  chords,  which  is  regulated  by  muscular 


SOME   SOUND-WAVE  RECEIVERS.  287 

action.  The  cavities  of  the  mouth  and  the  nasal  passages 
form  a  compound  resonance-tube.  This  tube  adapts  it- 
self, by  its  varying  width  and  length,  to  the  pitch  of  the 
note  produced  by  the  vocal  chords.  Place  a  finger  on 
the  protuberance  of  the  throat  called  "  Adam's  apple," 
and  sing  a  low  note ;  then  sing  a  high  note,  and  you  will 
observe  that  the  protuberance  rises  in  the  latter  case,  thus 
shortening  the  distance  between  the  vocal  chords  and  the 
lips.  Set  a  tuning-fork  in  vibration,  open  the  mouth  as  if 
about  to  sing  the  corresponding  note,  place  the  fork  in 
front  of  it,  and  the  cavity  of  the  mouth  will  resound  to 
the  note  of  the  fork,  but  will  cease  to  do  so  when  the 
mouth  adapts  itself  to  the  production  of  some  other  note. 
The  different  qualities  of  the  different  vowel  sounds  are 
produced  by  the  varying  forms  of  the  resonating  mouth- 
cavity,  the  pitch  of  the  fundamental  tones  given  by  the 
vocal  chords  remaining  the  same.  This  constitutes  articu- 
lation. 


Section  XIII. 

SOME   SOUND-WAVE  RECEIVERS. 

27O.  The  Phonograph.  —  Figure  245  represents  the  Edison 
phonograph.  A  metallic  cylinder  A  is  rotated  by  means  of  a  crank.  On 
the  surface  of  the  cylinder  is  cut  a  shallow  helical  groove  running  around 
the  cylinder  from  end  to  end,  like  the  thread  of  a  screw.  A  small  metallic 
point,  or  style,  projecting  from  the  under  side  of  a  thin  metallic  disk  D 
(Fig.  246),  which  closes  one  orifice  of  the  mouth-piece  B,  stands  directly 
over  the  thread.  By  a  simple  device  the  cylinder,  when  the  crank  is 
turned,  is  made  to  advance  just  rapidly  enough  to  allow  the  groove  to 
keep  constantly  under  the  style.  The  cylinder  is  covered  with  tinfoil. 
The  cone  F  is  usually  applied  to  the  mouth-piece  to  concentrate  the  sound- 
waves upon  the  disk  D. 


288 


SOUND. 


Now,  when  a  person  directs  his  voice  toward  the  mouth-piece,  the  aerial 
waves  cause  the  disk  D  to  participate  in  every  motion  made  by  the  parti- 
cles of  air  as  they  beat  against  it,  and  the  motion  of  the  disk  is  communi- 


Fig.  245. 

cated  by  the  style  to  the  tinfoil,  producing  thereon  impressions  or  indenta- 
tions as  it  passes  on  the  rotating  cylinder.  The  result  is  that  there  is  left 
upon  the  foil  an  exact  representation  in  relief  of  every  movement  made  by 
the  style.  Some  of  the  indentations  are  quite  perceptible  to  the  naked 
eye,  while  others  are  visible  only  with 
the  aid  of  a  microscope  of  high  power. 
Figure  247  represents  a  piece  of  the  foil 
as  it  would  appear  inverted  after  the  in- 
dentations (here  greatly  exaggerated) 
have  been  imprinted  upon  it.  Fig.  246. 

The  words  addressed  to  the  phonograph  having  been  thus  impressed 
upon  the  foil,  the  mouth-piece  and  style  are  temporarily  removed,  while 
the  cylinder  is  brought  back  to  the  position  it  had 
when  the  talking  began,  and  then  the  mouth-piece 
is  replaced.    Now,  evidently,  if  the  crank  is  turned 
Fig.  247.  jn  ^ne  same  direction  as  before,  the  style,  resting 

upon  the  foil  beneath,  will  be   made  to  play  up  and  down  as  it  passes 
over  ridges   and   sinks  into   depressions;   this  will  cause  the  disk  D  to 


SOME   SOUND-WAVE   RECEIVERS. 


289 


reproduce  the  same  vibratory  movements  that  caused  the  ridges  and 
depressions  in  the  foil.  The  vibrations  of  the  disk  are  communicated 
to  the  air,  and  through  the  air  to  the  ear ;  thus  the  words  spoken  to  the 
apparatus  may  be,  as  it  were,  shaken  out  into  the  air  again  at  any  subse- 
quent time,  even  centuries  after,  accompanied  by  the  exact  accents,  into- 
nations, and  quality  of  sound  of  the  original. 

271.  The  Ear.  —  In  Figure  248,  A  represents  the  external  ear-passage; 
a  is  a  membrane,  called  the  tympanum,  stretched  across  the  bottom  of  the 
passage,  and  thus  closing  the  orifice  of  a  cavity  b,  called  the  drum  ;  c  is  a 


Fig.  348* 

chain  of  small  bones  stretching  across  the  drum,  and  connecting  the 
tympanum  with  the  thin  membranous  wall  of  the  vestibule  e;  ff  are  a 
series  of  semicircular  canals  opening  into  the  vestibule;  g  is  the  open- 
ing into  another  canal  in  the  form  of  a  snail-shell  /,  hence  called  the 
cochlea  (this  is  drawn  on  a  reduced  scale)  ;  d  is  a  tube  (the  Eustachian 
tube'}  connecting  the  drum  with  the  throat;  and  h  is  the  auditory  nerve. 
The  vestibule  and  all  the  canals  opening  into  it  are  filled  with  a  trans- 
parent liquid.  The  drum  of  the  ear  contains  air,  and  the  Eustachian  tube 
forms  a  means  of  ingress  and  egress  for  air  through  the  throat. 

Now  how  does  the  ear  hear  ?  and  how  is  it  able  to  distinguish  between 
the  infinite  variety  of  form,  rapidity,  and  intensity  of  aerial  sound-waves 


290  SOUND. 

so  as  to  interpret  correctly  the  corresponding  quality,  pitch,  and  loudness 
of  sound  1  Sound-waves  enter  the  external  ear-passage  A  as  ocean-waves 
enter  the  bays  of  the  seacoast,  are  reflected  inward,  and  strike  the  tym- 
panum. The  air-particles,  beating  against  this  drum-head,  impress  upon 
it  the  precise  wave-form  that  is  transmitted  to  it  through  the  air  from  the 
sounding  body.  The  motion  received  by  the  drum-head  is  transmitted 
by  the  chain  of  bones  to  the  membranous  wall  of  the  vestibule.  From 
the  walls  of  the  spiral  passage  of  the  cochlea  project  into  its  liquid  con- 
tents thousands  of  fine  elastic  threads  or  fibres,  called  "  rods  of  Corti." 
As  the  passage  becomes  smaller  and  smaller,  these  vibratile  rods  become 
of  gradually  diminishing  length  and  size  (such  as  the  wires  of  a  piano 
may  roughly  represent),  and  are  therefore  suited  to  respond  sympatheti- 
cally to  a  great  variety  of  vibration-periods.  This  arrangement  is  some- 
times likened  to  a  "harp  of  three  thousand  strings"  (this  being  about 
the  number  of  rods).  The  auditory  nerve  at  this  extremity  is  divided 
into  a  large  number  of  filaments,  like  a  cord  unravelled  at  its  end,  and 
one  of  these  filaments  is  attached  to  each  rod.  Now,  as  the  sound- 
waves reach  the  membranous  wall  of  the  vestibule,  they  set  it,  and  by 
means  of  it  the  liquid  contents,  into  forced  vibration,  and  so  through  the 
liquid  all  the  fibres  receive  an  impulse.  Those  rods  whose  vibration 
periods  correspond  with  the  periods  of  the  constituents  forming  the  com- 
pound wave  are  thrown  into  sympathetic  vibration.  The  rods  stir  the 
nerve  filaments,  and  the  nerve  transmits  to  the  brain  the  impressions  re- 
ceived. Just  as  a  piano  when  its  dampers  are  raised  and  a  person  sings 
into  it,  may  be  said  to  analyze  each  sound-wave,  and  show  by  the  vibrat- 
ing strings  of  how  many  tones  it  is  composed,  as  well  as  their  respective 
pitch,  and  by  the  amplitude  of  their  vibrations  their  respective  intensi- 
ties ;  so,  it  is  thought,  this  wonderful  harp  of  the  ear  analyzes  every  com- 
plex sound-wave  into  a  series  of  simple  vibrations.  Tidings  of  the  dis- 
turbances are  communicated  to  the  brain,  and  there,  in  some  mysterious 
manner,  these  disturbances  are  interpreted  as  sound  of  definite  quality, 
pitch,  and  intensity. 


CHAPTER  VIII. 
RADIANT  ENERGY,  ETHER-WAVES,  — LIGHT. 

Section  I. 

INTRODUCTION. 

272.  Energy  Received  from  the  Sun.  —  Exposed  to 
the  sun,  the  skin  is  warmed,  —  the  sense  of  touch  is 
affected;  it  is  illuminated,  —  thereby  the 
sense  of  sight  is  affected ;  it  is  tanned,  — 
its  chemical  condition  is  changed.  It  is 
evident  that  we  receive  something  which 
must  come  to  us  from  the  sun.  To  the 
sense  of  touch  it  appears  to  be  heat;  in 
the  eye  it  produces  the  sensation  of  light ; 
in  certain  substances  it  has  the  power  to 
produce  chemical  changes.  What  is  it  that 
we  receive  from  the  sun? 

Figure  249  represents  an  instrument 
called  a  radiometer.  The  moving  part  is 
a  small  vane  resting  on  the  point  of  a 
needle.  It  is  so  nicely  poised  on  this  pivot 
that  it  rotates  with  the  greatest  freedom.  Fig-  249* 
To  the  extremities  of  each  of  the  four  arms  of  the  vane 
are  attached  disks  of  aluminum,  which  are  white  on  one 
side  and  black  on  the  other.  The  whole  is  enclosed  in  a 
glass  bulb,  and  the  air  within  is  reduced  to  less  than  one- 
millionth  its  usual  density.  If  the  instrument  is  exposed 


292  KADIANT   ENERGY. 

to  the  sun  the  wheel  will  rotate  with  the  white  faces  in 
advance. 

In  just  what  manner  it  is  caused  to  rotate  does  not  con- 
cern us  at  present ;  but  the  fact  that  it  rotates,  and  that 
it  is  caused  to  rotate  directly  or  indirectly  by  something 
that  comes  from  the  sun,  is  pertinent  to  the  question  be- 
fore us.  Whenever  a  body  is  caused  to  move  or  increase 
its  rate  of  motion,  energy  must  be  imparted  to  it;  hence 
energy  must  be  imparted  to  the  radiometer-vane  by  the  sun. 

That  which  we  receive  from  the  sun,  whether  it  affects 
the  sense  of  touch  or  of  sight,  or  produces  chemical  changes, 
is  in  reality  some  form  of  energy  and  is  one  and  the  same 
form  whatever  the  effect. 

273.  The  Ether.  —  If  we  receive  the  energy  of 
motion,  what  moves  ?  Our  atmosphere  is  but  a  thin 
mantle  covering  the  earth,  while  the  great  space  that 
separates  us  from  the  sun  contains  no  air  or  other  known 
substance.  But  empty  space  cannot  communicate  motion. 
It  is  assumed  —  it  is  necessary  to  assume  —  that  there  is 
some  medium  filling  the  interplanetary  space  ;  in  fact, 
filling  all  space  otherwise  unoccupied,  a  medium  by  which 
motion  can  be  communicated  from  one  point  to  another. 
This  medium  has  received  the  name  of  the  ether. 

We  cannot  see,  hear,  feel,  taste,  smell,  weigh,  nor  meas- 
ure it.  What  evidence,  then,  have  we  that  it  exists? 
This  :  phenomena  occur  just  as  they  would  occur  if  all 
space  were  filled  with  an  ethereal  medium  capable  of 
transmitting  motion  ;  we  have  been  able  to  account  for 
these  phenomena  on  no  other  hypothesis,  hence  our  belief 
in  the  existence  of  the  medium. 

The  transmission  of  energy  through  the  medium  of  the 
ether  is  called  radiation;  energy  so  transmitted  is  called 


UNDULATORY   THEORY.  293 

radiant  energy,  and  the  body  emitting  energy  in  this 
manner  is  called  a  radiator. 

274.  Undulatory  Theory;    the  Sensation  of   Sight. 

—  All  evidence  points  to  one  conclusion  :  that  we  receive 
energy  from  the  sun  in  the  form  of  vibrations  or  waves; 
that  a  portion  of  these  waves  having  suitable  wave-length 
are  capable  of  causing  through  the  eye  the  sensation  of 
sight.  Such  as  affect  the  sense  of  sight  are  called  light- 
waves.1 This  is  known  as  the  undulatory  theory  of  light. 
The  term  light  is  commonly  applied  to  those  ether-waves 
which  are  capable  of  producing  the  sensation  of  sight ; 
hence  light  is  that  vibration  of  the  ether  which  may  be 
appreciated  by  the  organ  of  sight. 

275.  Sources    of  Light- waves,    Incandescence    and 
Phosphorescence.  —  Every  form  of   matter  when  suffi- 
ciently heated  emits  light-waves  ;  in  other  words,  when 
the  vibration  period  of  its  molecules  becomes  such  as  to 
create   ethereal  waves  that  are   capable  of  affecting  the 
sense  of  sight,  the  body  is  said  to  be  luminous.     This  con- 
dition is  termed  incandescence.     The  sun  and  fixed  stars 
are  in  a  condition  of  intense  incandescence.     Nearly  all 
the  artificial  sources  of  light-waves,  such  as  lamp  and  gas 
flames  and  electric  lamps,  depend  upon  the  development 
of  light-waves  mainly  through  the  incandescence  of  carbon. 


1  It  will  be  shown  further  on,  that  not  all  ether-way es  are  capable  of  affecting 
the  sight,  hence  for  the  purpose  of  distinction  we  apply  the  term  light- waves  to  those 
ether-waves  only  which  are  capable  of  producing  vision.  It  is  strongly  recommended 
that  the  student  in  beginning  this  branch  of  science  make  use  of  the  term  light-waves 
instead  of  light  except  when  such  usage  would  lead  to  an  inconvenient  circumlocu- 
tion, in  order  that  he  may  have  strongly  impressed  upon  his  mind  the  fact  that  when 
he  is  dealing  with  light  he  is  dealing  with  waves. 


294 


RADIANT   ENERGY. 


There  is  a  class  of  substances,  such  as  the  sulphides  of 
calcium,  strontium,  etc.,  which,  after  several  hours'  expos- 

ure  to  light-waves,  absorb  their 

energy  (i.e.  their  molecules  ac- 
quire sympathetic  vibrations) 
without  becoming  hot,  and  in 
turn  emit  light-waves,  which  are 
quite  perceptible  in  a  dark  room 
for  several  hours  after  the  ex- 
posure. This  property  of  shining 
in  the  dark  after  having  been 
.  exposed  to  light-waves  is  termed 
phosphorescence.  A  so-called  lumi- 
nous paint  is  prepared  and  ap- 
Fig.  250.  plied  to  certain  parts  of  bodies 

that  are  exposed  to  sunshine  during  the  day;  at  night 
those  parts  to  which  the  paint  is  applied  are  alone  lumi- 
nous. This  paint  may  be  used  for  a  variety  of  purposes, 
such  as  rendering  luminous  danger  signals,  door  numbers 
and  plates  (Fig.  250),  etc. 

276.    Light-waves   travel   in   Straight  Lines.  —  The 

path  of  light-waves  admitted  into  a  darkened  room  through 
a  small  aperture,  as  indicated  by  the  illuminated  dust,  is 
perfectly  straight.  An  object  is  seen  by  means  of  light- 
waves which  it  sends  to  the  eye.  A  small  object  placed  in 
a  straight  line  between  the  eye  and  a  luminous  point 
may  intercept  the  light-waves  in  that  path,  and  the  point 
become  invisible.  Hence  we  cannot  see  around  a  corner, 
or  through  a  bent  tube. 


277.    Ray,  Beam,  Pencil.  —  Any  line  RR,  Figure  251, 
which  pierces  the    surface  of   an   ether-wave  ab   perpen- 


RAY,   BEAM,   PENCIL.  295 

dicularly  is   called  a  ray.      The   term  "ray"  is   but  an 

expression  for  the*direction  in  which  motion  is  propagated, 

and  along  which  the  successive  effects  of  ether-waves  occur. 

If  the  wave-surface  a'b'  is  a  plane, 

the  rays  R/R'  are  parallel,  and  a 

collection  of  such  rays  is  called  a 

beam.     If  the  wave-surface  anb" 

is  spherical  or  concave,  the  rays 

R"R"  have  a  common  point  at 

the  center  of   curvature ;   and   a 

collection  of  such  rays  is  called 

a  pencil. 

278.  Transparent,    Translu- 
cent,    and     Opaque     Bodies. — 

Bodies  are  transparent,  translu- 
cent, or  opaque,  according  to 
the  manner  in  which  they  act 
upon  the  light-waves  which  pass 
through  them.  Generally  speak- 
ing, those  objects  are  transparent  that  allow  other  objects 
to  be  seen  through  them  distinctly,  e.g.  air,  glass,  and 
water.  Those  objects  are  translucent .  that  allow  light- 
waves to  pass,  but  in  such  a  scattered  condition  that 
objects  are  not  seen  distinctly  through  them,  e.g.  fog, 
ground  glass,  and  oiled  paper.  Those  objects  are  opaque 
that  apparently  cut  off  all  the  light-waves  and  prevent 
objects  from  being  seen  through  them. 

279.  Luminous    and    Illuminated   Objects.  —  Some 
bodies  are  seen  by  means  of  light-waves  which  they  emit, 
e.g.  the  sun,  a  candle  flame,  and  a  "  live  "  coal ;  they  are 
called  luminous   bodies.     Other  bodies   are  seen  only  by 


296  RADIANT  ENERGY. 

means  of  light-waves  which  they  receive  from  luminous 
ones;  and  when  thus  rendered  visible  are  said  to  be 

illuminated,  e.g.  the  moon,  a 
man,  a  cloud,  and  a  "dead" 
coal. 

Every  point  of  a  luminous 
body  is  an  independent  source  of 
light-waves,  and  emits  light-ivaves 
in  every  direction.  Such  a  point 
is  called  a  luminous  point.  In 
Figure  252  there  are  represented 
a  few  of  the  infinite  number  of 
Fig.  353.  pencils  emitted  by  three  lumi- 

nous points  of  a  candle  flame.  Every  point  of  an  illumi- 
nated object,  db,  receives  light-waves  from  every  luminous 
point. 

28O.  Images  formed  through  Small  Apertures. 

Experiment  191. —  Cut  a  hole  about  4  inches  square  in  one  side  of 
a  box ;  cover  the  hole  with  tin-foil,  and  prick  a  hole  in  the  foil  with  a 
pin.  Place  the  box  in  a  darkened  room,  and  a  candle  flame  in  the  box 
near  to  the  pin-hole.  Hold  an  oiled-paper  screen  before  the  hole  in 
the  foil ;  an  inverted  image  of  the  candle  flame  will  appear  upon  the 
translucent  paper. 

An  image  is  a  kind  of  picture  of  an  object.  If  light- 
waves from  objects  illuminated  by  the  sun,  e.g.  trees, 
houses,  clouds,  or  even  an  entire  landscape,  are  allowed 
to  pass  through  a  small  aperture  in  a  window  shutter 
and  strike  a  white  wall  in  a  dark  room,  inverted  im- 
ages of  the  objects  in  their  true  colors  will  appear  upon 
it.  The  cause  of  these  phenomena  is  easily  understood. 
When  no  screen  intervenes  between  the  candle  and  the 
screen  A,  Figure  253,  every  point  of  the  screen  receives 


SHADOWS.  297 

light-waves  from  every  point  of  the  candle ;  consequently, 
on  every  point  on  A,  im- 
ages of  the  infinite  num- 
ber of  points  of  the  candle 
are  formed.  The  result 
of  the  confusion  of  images 
is  equivalent  to  no  image. 
But  let  the  screen  B, 
containing  a  small  hole, 
be  interposed ;  then,  since  Fig.  253. 

light- waves  travel  only  in  straight  lines,  the  point  Y' 
can  only  receive  an  image  of  the  point  Y,  the  point  Z' 
only  of  the  point  Z,  and  so  for  intermediate  points; 
hence  a  distinct  image  of  the  object  must  be  formed  on 
the  screen  A. 

That  an  image  may  be  distinct,  the  rays  from  different 
points  of  the  object  must  not  mix  on  the  image,  but  all  rays 
from  each  point  on  the  object  must  be  carried  to  its  own 
point  on  the  image. 

281.   Shadows. 

Experiment  192. —Procure  two  pieces  of  tin  or  cardboard,  one 
18cm  square,  the  other  3cm  square.  Place  the.first  between  a  white 
wall  and  a  candle  flame  in  a  darkened  room.  The  opaque  tin  inter- 
cepts the  light-waves  that  strike  it,  and  thereby  excludes  light-waves 
from  a  space  behind  it. 

This  space  is  called  a  shadow.  That  portion  of  the  sur- 
face of  the  wall  that  is  darkened  is  a  section  of  the  shadow, 
and  represents  the  form  of  a  section  of  the  body  that 
intercepts  the  light-waves.  A  section  of  a  shadow  is  fre- 
quently for  convenience  called  a  shadow.  Notice  that  the 
shadow  is  made  up  of  two  distinct  parts,  —  a  dark  center 
bordered  on  all  sides  by  a  much  lighter  fringe.  The 


298  RADIANT  ENEEGY. 

dark  center  is  called  the  umbra,  and  the  lighter  envelope 
is  called  the  penumbra. 

Experiment  193.  —  Carry  the  tin  nearer  the*  wall,  and  notice  that 
the  penumbra  gradually  disappears  and  the  outline  of  the  umbra  be- 
comes more  distinct.  Employ  two  candle  flames,  a  little  distance  apart, 
and  notice  that  two  shadows  are  produced.  Move  the  tin  toward  the 
wall,  and  the  two  shadows  approach  one  another,  then  touch,  and 
finally  overlap.  Notice  that  where  they  overlap  the  shadow  is  deepest. 
This  part  gets  no  light-waves  from  either  flame,  and  is  a  section  of 
the  umbra;  while  the  remaining  portion  gets  light-waves  from  one 
or  the  other,  and  is  a  section  of  the  penumbra.  Or  move  the  eye 
across  the  shadow  from  side  to  side  and  see  parts  of  the  flame  in  the 
penumbra,  but  none  in  the  umbra. 

Just  so  the  umbra  of  every  shadow  is  the  part  that  gets  no 
light-waves  from  a  luminous  body,  while  the  penumbra  is 
the  part  that  gets  light-waves  from  some  portion  of  the  body, 
but  not  from  the  whole. 

Experiment  194.  —  Repeat  the  above  experiments,  employing  the 
smaller  piece  of  tin,  and  note  all  differences  in  phenomena  that  occur. 
Hold  a  hair  in  the  path  of  the  sun's  waves,  about  a  quarter  of  an  inch 
in  front  of  a  fly-leaf  of  this  book,  and  observe  the  shadow  cast  by 
the  hair.  Then  gradually  increase  the  distance  between  the  hair 
and  the  leaf,  and  note  the  change  of  phenomena. 

If  the  source  of  light-waves  were  a  single  luminous  point,  as  A  (Fig. 

_,    254),  the  shadow  of  an  opaque  body  B 

— "=as^  ^    would  be  of  infinite  length,  and  would 

consist  only  of  an  umbra.     But  if  the 
source  of  light-waves  has  a  sensible  size, 
254.  the  opaque  body  will  intercept  just  as 

many  separate  pencils  as  there  are  luminous  points,  and  consequently  will 
cast  an  equal  number  of  independent  shadows. 

Let  AB  (Fig.  255)  represent  a  luminous  body,  and  CD  an  opaque  body. 
The  pencil  from  the  luminous  point  A  will  be  intercepted  between  the 
lines  CF  and  DG,  and  the  pencil  from  B  will  be  intercepted  between  the 


INTENSITY    OF    ILLUMINATION,    ETC. 


299 


wave-lines  CE  and  DF.     Hence  the  light-waves  will  be  wholly  excluded 
only  from  the  space  between  the  lines  OF  and  DF,  which  enclose  the 


Fig.  355. 

umbra.  The  enveloping  penumbra,  a  section  of  which  is  included  between 
the  lines  CE  and  CF,  and  between  DF  and  DG,  receives  light-waves  from 
certain  points  of  the  luminous  body,  but  not  from  all. 


,  QUESTIONS.      « 

1.  What  do  you  understand  by  radiant  energy  ? 

2.  State  some  of  the  immediate  effects  which  radiant  energy  is 
capable  of  producing. 

3.  How  do  light-waves  originate  ? 

4.  a.  Has  a  ray  of  light  a  physical  existence?     b.  What  is   a 
light-wave  ? 

5.  a.  Does  a  "  dead "  coal  emit  ether-waves  ?     b.  Does  it  emit 
light-waves  ? 

6.  a.    When  is  a  body  said  to  be  incandescent  ?     b.    How  may  a 
non-luminous  body  be  rendered  incandescent  ? 

7.  Why  are  images  formed  through  apertures  inverted  ? 

8.  Why  is  the  size  of  the  image  dependent  on  the  distance  of  the 
screen  from  the  aperture  ? 

9.  Why  does  an  image  become  dimmer  as  it  becomes  larger? 

10.   Why  do  we  not  perceive  an  image  of  our  persons  on  every 
object  in  front  of  which  we  stand  ? 


300  RADIANT   ENERGY. 

11.  Upon  what  fact  does  a  gunner  rely  in  taking  sight? 

12.  Explain  the  umbra  and  penumbra  cast  by  the  opaque  body 
H  I,  Figure  255. 

13.  When  will  a  transverse  section  of  the  umbra  of  an  opaque 
body  be  larger  than  the  object  itself  ? 

14.  When  has  an  umbra  a  limited  length  ? 

15.  What  is  the  shape  of  the  umbra  cast  by  the  sphere  C  D, 
Figure  255  ? 

16.  If  C  D  should  become  the  luminous  body,  and  A  B  a  non- 
luminous  opaque  body,  what  changes  would  occur  in  the  umbra  and 
the  shadow  cast  ? 

17.  Why  is  it  difficult  to  determine  the  exact  point  on  the  ground 
where  the  umbra  of  a  church-steeple  terminates  ? 

18.  What  is  the  shape  of  a  section  of  the  shadow  cast  by  a 
circular  disk  placed  obliquely  between  a  luminous  body  and  a  screen  ? 
What  is  its  shape  when  the  disk  is  placed  edgewise  ? 

19.  Describe  the  shadow  cast  by  the  earth. 


Section   II. 

INTENSITY    OF     ILLUMINATION,     PHOTOMETRY,    VELOCITY 
OF   LIGHT-WAVES. 

282.  Unit    of  Measurement.  —  The    unit   generally 
employed  for  the   measurement  of  the   intensity  of  the 
light  emitted  by  a  luminous  body  is  the  British  candle 
power.     It  is  the  intensity  of  light  emitted  by  a  sperm 
candle  J  in.  in  diameter,  burning  120  grains  to  the  hour. 

283.  Diminution  of  Intensity  of  Illuminating  Capac- 
ity with  Distance.     Application  of  the  Law  of  Inverse 
Squares  to  Light.  —  Light  diminishes  in   intensity,  and 


INTENSITY   OF  ILLUMINATION,    ETC.  301 

hence  in  its  power  to  illuminate  objects  which  it  strikes, 
as  it  recedes  from  its  source.  The  intensity  of  light 
diminishes  as  the  square  of  the  distance  from  its  source 
increases.  Calling  the  quantity  of  light  falling  upon  a 
visiting  card  at  a  distance  of  2  feet  from  a  lamp  flame  1, 
the  quantity  falling  upon  the  same  card  at  a  distance  of 
4  feet  is  J,  at  a  distance  of  6  feet  it  is  l,  and  so  on.  This 
is  the  meaning  of  the  law  of  inverse  squares,  as  applied  to 
light. 

This  law  may  be  illustrated  thus  :   A  square  card  placed  (say)  1  foot 
from  a  certain  point  in  a  candle  flame,  as  at  A  (Fig.  256),  receives  from 
this  point  a  certain   quantity  of  light.     The 
same  light  if  not  intercepted  would  go  on  to 

B,  at  a  distance  of  2  feet,  and  would  there 
illuminate  four  squares,  each  of  the  size  of  the 
card,  and  being  spread  over  four  times  the 
area  can  illuminate  each  square  with  only  one 

fourth  the  intensity.     If  allowed  to  proceed  to    '  Fi 

C,  3  feet  distant,   it  illuminates   nine  such 

squares,  and  has  but  one  ninth  its  intensity  at  A.  The  law  is  strictly 
true  only  when  distance  from  individual  points  is  considered. 

284.  Photometry.  —  The  law  just  established  enables 
us  to  compare  the  illuminating  power  of  one  light  with 
that  of  another,  and  to  express  by  numbers  their  relative 
illuminating  powers.     The  process  is    called  photometry 
(light-measuring)  ;      and    the     instrument    employed,    a 
photometer. 

285.  The  Bunsen  Photometer  (Fig.  257)  has  a  screen 
of  paper  S,  mounted  in  a  box  B,  open  in  front  and  at 
the  two  ends.     The  box  slides  on  a  graduated  bar.     The 
screen  has  a  circular  central  spot  saturated  with  paraffine, 
which  renders  the  spot  more  translucent  than  other  por- 


302 


RADIANT   ENERGY. 


tions  of  the  screen.  One  side  of  the  screen  is  illuminated 
by  the  light  L,  whose  intensity  is  to  be  measured,  and 
the  other  side  by  a  standard  candle  L'.  When  the  screen 


Fig.  257. 

is  so  placed  that  the  two  sides  are  equally  illuminated 
by  the  two  lights,  the  paraffined  spot  becomes  nearly 
invisible.  When  one  side  is  more  strongly  illuminated 
than  the  other,  the  spot  appears  dark  on  that  side  and 

light  on  the  other.    The 
candle  power  of  the  two 
•*—  lights  is  directly  propor- 

tional to  the  square  of 
their  respective  distances 
from  the  screen  when  it 
is  equally  illuminated  on 
both  sides. 


Fig.  358. 


In  order  to  render  both  sides  of  the  disk  simultaneously  visible,  two 
mirrors,  m  and  m'  (Fig.  258),  are  placed  in  the  box  in  a  vertical  position, 
so  as  to  reflect  images  of  the  circular  spot  in  the  screen  S  to  the  eyes  at 
E,  EL 

QUESTIONS. 

1.  Suppose  that  a  lighted  candle  is  placed  in  the  center  of  each  of 
three  cubical  rooms,  respectively  10,  20,  and  30  feet  on  a  side ;  would 
a  single  wall  of  the  first  room  receive  more  light  than  a  single  wall 
of  either  of  the  other  rooms,  or  less  ? 


INTENSITY    OF    ILLUMINATION,    ETC.  303 

2.  Would  one  square  foot  of  a  wall  of  the  third  room  receive  as 
much  light  as  would  be  received  by  one  square  foot  of  a  wall  of  the 
first  room?     If  not,  what  difference  would  there  be,  and  why  the 
difference  ? 

3.  Give  a  reason  for  the  law  of  inverse  squares. 

4.  To  what  besides  light  has  this  law  been  found  applicable? 

286.  Visual  Angle. — We  see  an  object  by  means  of  its 
image  formed  on  the  retina  of  the  eye  ;  and  its  apparent 
magnitude  is  determined  by  the  extent  of  the  retina 
covered  by  its  image.  Rays  proceeding  from  opposite 
extremities  of  an  object,  as  AB  (Fig.  259),  meet  and  cross 


Fig.  259. 

one  another  in  the  window  of  the  eye,  called  the  pupil. 
Now,  as  the  distance  between  the  points  of  the  blades  of  a 
pair  of  scissors  depends  upon  the  angle  that  the  handles 
form  with  one  another,  so  the  size  of  the  image  formed  on 
the  retina  depends  upon  the  size  of  the  *  angle,  called  the 
visual  angle,  formed  by  these  rays  as  they  enter  the  eye. 
But  the  size  of  the  visual  angle  diminishes  as  the  distance 
of  the  object  from  the  eye  increases,  as  shown  in  the 
diagram  ;  e.g.  at  twice  the  distance  the  angle  is  one-half 
as  great  ;  at  three  times  the  distance  the  angle  is  one- 
third  as  great ;  and  so  on.  Hence,  distance  affects  the 
apparent  size  of  an  object.  Our  judgment  of  size  is, 
however,  influenced  by  other  things  besides  the  visual 
angle  which  the  object  subtends. 


304  RADIANT   ENERGY. 

287.  Velocity  of  Light- Waves.  —  By  several  ingenious 
methods  it  has  been  ascertained  that  light-waves  travel  at 
the  rate  of  about  186,000  miles  in  a  second,  a  velocity 
which  would  enable  them  to  go  around  the  earth  about 
seven  times  in  a  second.     Sound-waves  travel  in  air  at  the 
rate  of  only  about  one-fifth  of  a  mile  per  second.     This 
great  difference  can  be  accounted  for  only  on  the  suppo- 
sition that  the  rarity  and  elasticity  of  ether  are  enormously 
greater  than  that  of  air. 

Section  III. 

REFLECTION   OF   LIGHT-WAVES. 

288.  Law  of  Reflection. 

Experiment  195.  —  Look  through  the  hole  in  the  metal  band  (Fig. 
260),  marked  zero,  at  the  mirror.  You  see  in  the  mirror  an  image  of 

the  hole  through  which  you 
are  looking,  but  you  do  not 
see  the  image  of  any  of 
the  other  holes.  Rays  that 
pass  through  this  hole  strike 
the  mirror  perpendicularly, 
Fig.  260.  an(j  are  cai}ed  incident  rays. 

The  reflected  rays  are  thrown  back  in  the  same  line  and  through  the 
same  hole  that  the  incident  rays  travel  to  the  eye. 

Hold  a  candle  flame  at  one  of  the  other  holes  (or  stop  it  with  a  fin- 
ger), e.g.  at  the  hole  marked  10.  You  can  see  the  reflected  rays  of  the 
candle  flame  only  through  the  hole  of  the  same  number  on  the  other 
side,  i.e.  for  example,  incident  rays  making  an  angle  of  10°  (called  the 
angle  of  incidence)  with  the  perpendicular  to  the  surface  of  the  mirror 
is  reflected  at  an  angle  of  10°  (called  the  angle  of  reflection)  with  the 
perpendicular.  The  angle  of  reflection  is  always  equal  to  the  angle  of 
incidence. 


REFLECTION   OF  LIGHT-WAVES.  305 

289.  Reflection  from  Plane  Mirrors;  Virtual  Im- 
ages. —  MM  (Fig.  261)  represents 
a  plane  mirror,  and  AB  a  pencil  of 
divergent  rays  proceeding  from  the 
point  A  of  an  object  AH.  Erect- 
ing perpendiculars  at  the  points  of 
incidence,  or  the  points  where  these 
rays  strike  the  mirror,  and  mak- 
ing the  angles  of  reflection  equal 
to  the  angles  of  incidence,  the 
paths  BC  and  EC  of  the  reflected 
rays  are  found.  Fis- 

It  appears  that  divergent  incident  rays  remain  divergent 
after  reflection  from  a  plane  mirror.  (In  like  manner  con- 
struct a  diagram,  and  show  that  parallel  incident  rays  are 
parallel  after  reflection.)  Construct  another  diagram,  and 
show  that  convergent  incident  rays  are  convergent  after  re- 
flection, i.e.  reflection  from  a  plane  surface  does  not  alter 
the  angle  between  rays.  To  an  eye  placed  at  C,  the  points 
from  which  the  rays  appear  to  come  are  of  course  in  the 
direction  of  the  rays  as  they  enter  the  eye.  These  points 
may  be  found  by  continuing  the  rays  CB  and  CE  behind 
the  mirror,  till  they  meet  at  the  points  D*  and  N.  Every 
point  of  the  object  AH  sends  out  its  pencil  of  rays ;  and 
those  that  strike  the  mirror  at  a  suitable  angle  to  be 
reflected  to  the  eye,  produce  on  the  retina  of  the  eye  an 
image  of  that  point,  and  the  point  from  which  the  light- 
waves appear  to  emanate  is  found,  as  previously  described. 
Thus,  the  pencils  EC  and  BC  appear  to  emanate  from  the 
points  N  and  D ;  and  the  whole  body  of  light-waves  re- 
ceived by  the  eye  seems  to  come  from  an  apparent  object 
ND  behind  the  mirror.  This  apparent  object  is  called  an 
image;  but  as,  of  course,  there  can  be  no  real  image 


306  RADIANT   ENERGY. 

formed  there,  it  is  called  a  virtual  or  an  imaginary  image. 
It  will  be  seen,  by  construction,  that  an  image  in  a  plane 
mirror  appears  as  far  behind  the  mirror  as  the  object  is  in 
front  of  it,  and  is  of  the  same  size  and  shape  as  the  object. 

29O.   Reflection  from  Concave  Mirrors.  —  Let    MM' 

(Fig.  262),  represent  a  section  of  a  concave  mirror,  which 
may  be  regarded  as  a  small  part  of  a  hollow  spherical 
shell  having  a  polished  interior  surface.  The  distance 
MM'  is  called  the  diameter  of  the  mirror.  C  is  the  center 

of  the  sphere,  and  is 
called  the  center  of 
curvature.  G  is  the 
vertex  of  the  mirror. 
A  straight  line  DG 
drawn  through  the 
center  of  curvature 
and  the  vertex  is 
Fig.  262.  called  the  principal 

axis  of  the  mirror.  A  concave  mirror  may  be  considered 
as  made  up  of  an  infinite  number  of  small  plane  surfaces. 
All  radii  of  the  mirror,  as  CA,  CG,  and  CB,  are  perpen- 
dicular to  the  small  planes  which  they  strike.  If  C  be  a 
luminous  point,  it  is  evident  that  all  light-waves  emanating 
from  this  point,  and  striking  the  mirror,  will  be  reflected 
to  its  source  at  C. 

Let  E  be  any  luminous  point  in  front  of  a  concave 
mirror.  To  find  the  direction  that  rays  emanating  from 
this  point  take  after  reflection,  draw  any  two  lines  from 
this  point,  as  EA  and  EB,  representing  two  of  the  infi- 
nite number  of  rays  composing  the  divergent  pencil  that 
strikes  the  mirror.  Next,  draw  radii  to  the  points  of  inci- 
dence A  and  B,  and  draw  the  lines  AF  arid  BF,  making 


REFLECTION   OF   LIGHT-WAVES.  307 

the  angles  of  reflection  equal  to  the  angles  of  incidence. 
Place  arrow-heads  on  the  lines  representing  rays  to  indi- 
cate the  direction  of  the  motion.  The  lines  AF  and  BF 
represent  the  direction  of  the  rays  after  reflection. 

It  will  be  seen  that  the  rays  after  reflection  are  con- 
vergent, and  meet  at  the  point  F,  called  the  focus.  This 
point  is  the  focus  of  all  reflected  rays  that  emanate  from 
the  point  E.  It  is  obvious  that  if  F  were  the  luminous 
point,  the  lines  AE  and  BE  would  represent  the  reflected 
rays,  and  E  would  be  the  focus  of  these  rays.  Since  the 
relation  between  the  two  points  is  such  that  light-waves 
emanating  from  either  one  are  brought  by  reflection  to  a 
focus  at  the  other,  these  points  are  called  conjugate  foci.  Con- 
jugate foci  are  two  points  so  related  that  the  image  of  either  is 
formed  at  the  other.  The  rays  EA  and  EB  emanating  from 
E  are  less  divergent  than  rays  FA  and  FB,  emanating  from 
a  point  F  less  distant  from  the  mirror,  and  striking  the 
same  points.  Rays  emanating  from  D,  and  striking  the 
same  points  A  and  B,  will  be  still  less  divergent ;  and  if 
the  point  D  were  removed  to  a  distance  of  many  miles, 
the  rays  incident  at  these  points  would  be  very  nearly 
parallel.  Hence  rays  may  be  regarded 
as  practically  parallel  when  their  source. 
is  at  a  very  great  distance,  e.g.  the  sun's 
rays.  If  a  sunbeam,  consisting  of  a 
bundle  of  parallel  rays,  as  EA,  DG, 
and  HB  (Fig.  263),  strike  a  concave  Fig. 

mirror  parallel  with  its  principal  axis,  these  rays  become 
convergent  by  reflection,  and  meet  at  a  point  (F)  in  the 
principal  axis.  This  point,  called  the  principal  focus,  is 
just  half-way  between  the  center  of  curvature  and  the 
vertex  of  the  mirror. 

On  the  other  hand,  it  is  obvious  that  divergent  rays 


308 


RADIANT   ENERGY. 


emanating  from  the  principal  focus   of  a   concave   mirror 
become  parallel  by  reflection. 

If  a  small  piece  of  paper  is  placed  at  the  principal  focus 
of  a  concave  mirror,  and  the  mirror  is  exposed  to  the  par- 
allel rays  of  the  sun,  the  paper  will  quickly  burn. 

Construct  a  diagram,  and  show  that  rays  proceeding 
from  a  point  between  the  principal  focus  and  the  mirror 
are  divergent  after  reflection,  but  less  divergent  than  the 
incident  rays.  Reversing  the  direction  of  the  rays  the 
same  diagram  will  show  that  convergent  rays  are  rendered 
more  convergent  by  reflection  from  concave  mirrors. 

The  general  effect  of  a  concave  mirror  is  to  increase  the 

convergence  or  to 
decrease  the  diver- 
gence of  incident 
rays. 

The  statement,  that 
parallel  rays  after  re- 
flection from  a  concave 
mirror  meet  at  the  prin- 
cipal focus,  is  only  ap- 
proximately true.  The 

Fig.  264.  smaller  the  diameter  of 

the  mirror,  the  more  nearly  true  is  the  statement.    It  is  strictly  true  only 
of  parabolic  mirrors.     Such  are  used  m  the  head-lights  of  locomotives. 

291.    Formation  of  Images. 

Experiment  196.  —  Hold  some  object,  e.g.  a  rose,  as  ab  (Fig.  264), 
a  few  feet  in  front  of  a  concave  mirror.  Looking  in  the  direction  of 
the  axis  of  the  mirror  you  see  a  small  inverted  image  AB  of  the  object 
between  the  center  of  curvature,  C,  of  the  mirror  and  its  principal 
focus  F. 

Evidently  if  AB  represent  an  object  placed  between  the  principal 
focus  and  center  of  curvature,  then  ab  will  represent  the  image  of  the 
object.  The  image  in  this  case  may  be  projected  upon  a  screen,  but 
it  will  not  be  so  bright  as  in  the  former  case,  because  the  light-waves 
are  spread  over  a  larger  surface. 


KEFLECTION   OF   LIGHT-WAVES.  309 

Experiment  197.  —  Place  a  candle  in  an  otherwise  dark  room  20 
feet  from  the  mirror,  catch  the  focused  light-waves  upon  a  paper 
screen,  and  show  that  the  focus  is  half-way  between  the  vertex  and 
the  center  of  curvature  of  the  mirror. 

Experiment  198.  —  Advance  the  distant  candle  flame  toward  the 
mirror,  moving  it  up  and  down.  (1)  Show  that  the  focus  advances  to 
meet  the  flame,  and  that  when  the  flame  is  raised,  the  focus  is  depressed, 
and  the  converse.  (2)  Show  that  when  the  flame  is  at  the  center  of 
curvature,  there  also  is  the  focus.  (3)  Show  that  when  the  flame  is  be- 
tween the  center  of  curvature  and  the  principal  focus,  the  focus  of  the 
flame  is  farther  away  than  the  center  of  curvature.  (4)  Show  that 
when  the  flame  is  at  the  principal  focus,  the  reflected  rays  are  parallel, 
or  the  focus  is  at  an  infinite  distance.  (5)  Show  that  when  the  flame  is 
still  nearer,  the  reflected  rays  diverge  and  appear  to  come  from  a  point 
behind  the  mirror.  (6)  Notice  that  in  all  cases  except  the  last  the  im- 
ages are  real  and  inverted,  and  that  in  all  cases  where  a  real  image  is 
formed,  the  flame  and  the  image  may  change  places. 

Experiment  199.  —  Form  a  real  image  of  the  flame  between  your- 
self and  the  mirror ;  view  the 
image  through  a  convex  lens 
(Fig.  284) ;  show  that  the  im- 
age can  be  magnified  by  a 
convex  lens,  and  thereby  illus- 
trate the  principle  of  an  astro- 
nomical reflecting  telescope. 

Construct  the  image  of 
an  object  placed  between  ms- 

tbe  principal  focus  and  the  mirror,  as  in  Figure  265.  It 
will  be  seen  in  this  case  that  a  pencil  of  rays  proceeding 
from  any  point  of  an  object,  e.g.  D,  has  no  actual  focus, 
but  appears  to  proceed  from  a  virtual  focus  D',  back  of  the 
mirror ;  and  so  with  other  points,  as  E.  The  image  of  an 
object  placed  between  the  principal  focus  and  the  mirror  is 
virtual,  erect,  larger  than  the  object,  and  is  back  of  the  mirror. 

292.  Convex  Mirrors.  —  The  general  effect  of  convex 
mirrors  is  to  separate  incident  rays.  In  them  all  images 
are  virtual,  erect,  and  smaller  than  the  objects. 


310  RADIANT  ENERGY. 

Section  IV. 

KEF  R  ACTION. 

293.    Introductory  Experiments. 

Experiment  200.  — Into  a  darkened  room  admit  a  sunbeam  so 
that  its  rays  may  fall  obliquely  on  the  bottom  of  the  basin  (Fig.  266), 

and  note  the  place  on  the  bottom 
where  the  edge  of  the  shadow  DE 
cast  by  the  side  of  the  basin  DC 
meets  the  bottom  at  E.  Then, 
without  moving  the  basin,  fill  it 
even  full  with  water  slightly  clouded 
with  milk  or  with  a  few  drops  of  a 
solution  of  mastic  in  alcohol.  It 
will  be  found  that  the  edge  of  the 
shadow  has  moved  from  I)E  to  DF, 
and  meets  the  bottom  at  F.  Beat 
a  blackboard  rubber,  and  create  a 
cloud  of  dust  in  the  path  of  the  beam  in  the  air,  and  you  will  dis- 
cover that  the  rays  GD  that  graze  the  edge  of  the  basin  at  D  be- 
come bent  at  the  point  where  they  enter  the  water,  and  now  move 
in  the  bent  line  GDF,  instead  of,  as  formerly,  in  the  straight  line  GE. 
The  path  of  the  line  in  the  water  is  now  nearer  to  the  vertical  side  DC  ; 
in  other  words,  this  part  of  the  beam  is  more  nearly  vertical  than  before. 
Experiment  201.  —  Place  a  coin  (A,  Fig.  267)  on  the  bottom  of 
an  empty  basin,  so  that,  as  you  look  through  a  small  hole  in  a  card 
BC  over  the  edge  of  the  vessel,  the  coin  is 
just  out  of  sight.  Then,  without  moving  the 
card  or  basin,  fill  the  latter  with  water.  Now, 
on  looking  through  the  aperture  in  the  card, 
the  coin  is  visible.  The  beam  AE,  which 
formerly  moved  in  the  straight  line  AD,  is 
now  bent  at  E,  where  it  leaves  the  water, 
and,  passing  through  the  aperture  in  the  card, 
enters  the  eye.  Observe  that,  as  the  beam 
passes  from  the  water  into  the  air,  it  is  turned  farther  from  a  verti- 


BEFR  ACTION.  311 

cal  line  EF ;  in  other  words,  the  beam  is  farther  from  the  vertical  than 
before. 

Experiment  202.  —  From  the  same  position  as  in  the  last  experi- 
ment, direct  the  eye  to  the  point  G  in  the  basin  filled  with  water. 
Reach  your  hand  around  the  basin,  and  place  your  finger  where  that 
point  appears  to  be.  On  examination,  it  will  be  found  that  your 
finger  is  considerably  above  the  bottom.  Hence,  the  effect  of  the  bend- 
ing of  rays,  as  they  pass  obliquely  out  of  water,  is  to  cause  the  bottom  to 
appear  more  elevated  than  it  really  is  ;  in  other  words,  to  cause  the  water 
to  appear  shallower  than  it  is. 

Experiment  203. —  Thrust  a  pencil  obliquely  into  water ;  it  will 
appear  shortened,  bent  at  the  surface  of  the  water,  and  the  immersed 
portion  elevated. 

Experiment  204. — Place  a  piece  of  wire  (Fig.  268)  vertically  in 
front  of  the  eye,  and  hold  a  narrow  strip  of  thick  plate  glass  horizon- 
tally across  the  wire,  so  that  the  light-waves  from  the  wire 
may  pass  obliquely  through  the  glass  to  the  eye.  The  wire 
will  appear  to  be  broken  at  the  two  edges  of  the  glass,  and 
the  intervening  section  will  appear  to  the  right  or  left  accord- 
ing to  the  inclination  of  the  glass ;  but  if  the  glass  is  not 
inclined  to  the  one  side  or  the  other,  the  wire  does  not 

Fig.  368. 

appear  broken. 

Experiment  205.  —  Partly  fill  a  cell1  with  parallel  glass  sides 
with  carbon  bisulphide,  then  add  water.  Place  the  cell  in  the  path 
of  a  beam  reflected  from  a  porte  lumiere.  Place  vertically  in  front  of 
the  cell  a  wire,  and  project  with  a  lens  a  shadow  of  the  wire  on  a 
screen.  Turn  the  cell  obliquely,  as  in  the  last  experiment,  and 
notice  the  difference  in  the  refracting  power  of  the  two  liquids. 

Experiment  206.  —  Partly  fill  the  same  cell  with  water.  Focus 
it  on  the  screen  so  that  the  surface  of  the  water  will  be  visible. 
Add  a  lump  of  ice  on  the  water.  Observe  the  streakiness  caused  by 
difference  in  the  density  of  water  at  different  temperatures. 

Experiment  207. — Project  with  a  lens  a  luminous  circle  on  a 
screen.  Hold,  a  few  feet  in  front  of  the  screen,  a  candle  flame  in  the 
path  of  the  light-waves.  Observe  the  wavy  streakiness  arising  from 
the  changing  density  of  the  air  and  convection  currents. 

1  These  cells,  used  with  stereopticons  for  projecting  liquids,  can  be  procured  of 
apparatus  dealers. 


312  RADIANT    ENERGY. 

When  a  light-beam  passes  from  one  medium  into  another  of  different 
density,  it  is  bent  or  refracted  at  the  boundary  plane  between  the  two 
media,  unless  it  falls  exactly  perpendicularly  on  this  plane.  If  it,  pass 
into  a  denser  medium,  it  is  refracted  toward  a  perpendicular  to  this  plane ; 
if  into  a  rarer  medium,  it  is  refracted  from  the  perpendicular.  The  angle 

GDO  (Fig.  266)  is  called  the  angle 
of  incidence ;  FDN,  the  angle  of  re- 
fraction; and  EDF,  the  angle  of 
deviation. 

294.  Cause  of  Refraction. 

—  Careful  experiments  have  proved  that 
the  velocity  of  light-waves  is  less  in  a 
dense  than  in  a  rare  medium.  Let  the 
series  of  parallel  lines  AB  (Fig.  269) 
represent  a  series  of  wave-fronts  leav- 
ing an  object  C,  and  passing  through 
a  rectangular  piece  of  glass  DE,  and 
constituting  a  beam.  Every  point 
in  a  wave-front  moves  with  equal 
Fig.  269.  velocity  as  long  as  it  traverses  the 

same  medium ;  but  the  point  a  of  a  given  wave  ab  enters  the  glass  first, 
and  its  velocity  is  impeded,  while  the  point  6  retains  its  original  velocity ; 
so  that,  while  the  point  a  moves  to  a',  b  moves  to  bf,  and  the  result  is 
that  the  wave-front  assumes  a  new  direction  (very  much  in  the  same 
manner  as  a  line  of  soldiers  execute  a  wheel),  and  a  ray  or  a  line  drawn 
perpendicularly  through  the  series  of  waves  is  turned  out  of  its  original 
direction  on  entering  the  glass.  Again,  the  extremity  c  of  a  given  wave- 
front  cd  first  emerges  from  the  glass,  when  its  velocity  is  immediately 
quickened ;  so  that,  while  d  advances  to  df,  c  advances  to  c',  and  the 
direction  of  the  ray  is  again  changed.  The  direction  of  the  ray,  after 
emerging  from  the  glass,  is  parallel  to  its  direction  before  entering  it,  but 
it  has  suffered  a  lateral  displacement.  Let  C  represent  a  section  of  the 
wire  used  in  Experiment  262,  and  the  cause  of  the  phenomenon  observed 
will  be  apparent.  If  the  beam  strike  the  glass  perpendicularly,  all  points 
of  the  wave  will  be  checked  at  the  same  instant  on  entering  the  glass ; 
consequently  it  will  suffer  no  refraction. 

295.  Index  of  Refraction.  —  The  deviation  of  light- 
waves, in  passing  from  one  medium  to  another,  varies 
with  the  medium  and  with  the  angle  of  incidence.  It 


UNIVERSITY  OF 


OF  PHYSfCS 

REFRACTION. 


318 


diminishes  as  the  angle  of  incidence  diminishes,  and  is 
zero  when  the  incident  ray  is  normal  (i.e.  perpendicular 
to  the  surface  of  the  medi- 
um). It  is  highly  impor- 
tant, knowing  the  angle 
of  incidence,  to  be  able  to 
determine  the  direction 
which  a  ray  will  take  on 
entering  a  new  medium. 
Describe  a  circle  around 
the  point  of  incidence  A 
(Fig.  270)  as  a  center; 
through  the  same  point 
draw  IH  perpendicular  to  Fis-  3>?0- 

the  surfaces  of  the  two  media,  and  to  this  line  drop  per- 
pendiculars BD  and  CE  from  the  points  where  the  circle 
cuts  the  ray  in  the  two  media.  Then  suppose  that  the 
perpendicular  BD  is  -£$  of  the  radius  AB  ;  now  this  frac- 
tion y^-  is  called  (in  trigonometry)  the  sine  of  the  angle 
DAB.  Hence,  T87  is  the  sine  of  the  angle  of  incidence. 
Again,  if  we  suppose  that  the  perpendicular  CE  is  T%  of 
the  radius,  then  the  fraction  -f$  is  the  sine  of  the  angle  of 
refraction.  The  sines  of  the  two  angles  are  to  one  another 
as  TV :  T%,  or  as  4 :  3.  The  quotient  (in  this  case  f  =  1.33+) 
obtained  by  dividing  the  sine  of  the  angle  of  incidence  by 
the  sine  of  the  angle  of  refraction  is  called  the  index  of 
refraction.  It  can  be  proved  to  be  the  ratio  of  the  velocity 
of  the  incident  to  that  of  the  refracted  light-waves.  It  is 
found  that  for  the  same  media  the  index  of  refraction  is 
a  constant  quantity  ;  i.e.  the  incident  ray  might  be  more 
or  less  oblique,  still  the  quotient  would  be  the  same. 

296.  Indices  of  Refraction.  —  The  index  of  refraction  for  light- 
waves in  passing  from  air  into  water  is  approximately  |,  and  from  air  into 


314 


RADIANT   ENERGY, 


glass  f ;  of  course,  if  the  order  is  reversed,  the  reciprocal  of  these  frac- 
tions must  be  taken  as  the  indices ;  e.g.  from  water  into  air,  the  index  is  f ; 
from  glass  into  air,  f .  When  a  ray  passes  from  a  vacuum  into  a  medium, 
the  refractive  index  is  greater  than  unity,  and  is  called  the  absolute  index 
of  refraction.  The  relative  index  of  refraction,  from  any  medium  A  into  another 
B,  is  found  by  dividing  the  absolute  index  of  B  by  the  absolute  index  of  A. 

The  refractive  index  varies  with  wave-length.    The  following  table  is 
intended  to  represent  mean  indices :  — 

TABLE  OF  ABSOLUTE  INDICES. 


Air  at  0°  C.,  and  760mm  pressure    .  1.000294 

Pure  water 1.33 

Alcohol 1.37 

Spirits  of  turpentine 1.48 

Humors  of  the  eye  (about)     .     .     .  1.35 


Carbon  bisulphide 1.641 

Crown  glass  (about) 1.53 

Flint  glass  (about) 1.61 

Diamond  (about) 2.5 

Lead  chromate 2.97 


297.    Critical    Angle;     Total    Reflection.  —  Let    SS' 

(Fig.  271)  represent  the  boundary  surface  between  two 
media,  and  AO  and  BO  incident  rays  in  the  more  refractive 
medium  (e.g.  glass) ;  then  OD  and  OE  may  represent  the 
same  rays  respectively  after  they  enter  the  less  refractive 


Fig.  371. 

medium  (e.g.  air).  It  will  be  seen  that,  as  the  angle  of 
incidence  is  increased,  the  refracted  ray  rapidly  approaches 
the  surface  OS.  Now,  there  must  be  an  angle  of  incidence 
(e.g.  COM)  such  that  the  angle  of  refraction  will  be  90° ; 


REFRACTION. 


315 


in  this  case  the  incident  ray  CO,  after  refraction,  will  just 
graze  the  surface  OS.  This  is  called  the  critical  or  limiting 
angle.  Any  incident  ray,  as  LO,  making  a  larger  angle 
with  the  normal  than  the  critical  angle,  cannot  emerge  from 
the  medium,  and  consequently  is  not  refracted.  Experi- 
ment shows  that  all  such  rays  undergo  internal  reflection ; 
e.g.  the  ray  LO  is  reflected  in  the  direction  ON.  Reflec- 
tion in  this  case  is  perfect,  and  hence  is  called  total  reflec- 
tion. Total  reflection  occurs  when  rays  in  the  more  refractive 
medium  are  incident  at  an  angle  greater  than  the  critical  angle. 

Surfaces  of  transparent  media,  under  these  circumstances,  constitute  the 
best  mirrors  possible.  The  critical  angle  diminishes  as  the  refractive  index 
increases.  For  water  it  is  about  48}°;  for  flint  glass,  38°  41' ;  and  for  the 
diamond,  23°  41'.  Light-waves  cannot,  therefore,  pass  out  of  water  into 
air  with  a  greater  angle  of  incidence  than  48|°.  The  brilliancy  of  gems, 
particularly  the  diamond,  is  due  in  part  to  their  extraordinary  power  of 
internal  reflection,  arising  from  their  large  indices  of  refraction. 

298.  Illustrations  of  Refraction  and  Total  Reflection. 

Experiment  208.  —  Observe  the  image  of  a  candle  flame  reflected 
by  the  surface  of  water  in  a  glass  beaker,  as  in  Figure  272. 

Experiment  209.  —  Thrust  the  closed  end  of  a  glass  test-tube 
(Fig.  273)  into  water,  and  incline  the  tube.  Look  down  upon  the 
immersed  part  of  the  tube,  and  its  upper  surface  will  look  like  bur- 


Fig.  273.  Fig.  273. 

nished  silver,  or  as  if  the  tube  contained  mercury.  Fill  the  test-tube 
with  water,  and  immerse  as  before  ;  the  total  reflection  which  before 
occurred  at  the  surface  of  the  air  in  the  submerged  tube  now 
disappears.  Explain. 


316 


RADIANT    ENERGY. 


Section  V. 


DOUBLE    REFRACTION. 

299.    Double  Kefraction. 

Experiment  210.  —  Through  a  card  make  a  pin-hole,  and  hold 
the  card  so  that  you  may  see  the  sky 
through  the  hole.  Now  bring  a  crystal  of 
Iceland  spar  (Fig.  274)  between  the  eye 
and  the  card,  and  look  at  the  hole  through 
two  parallel  surfaces  of  the  crystal.  There 
will  appear  to  be  two  holes,  with  light- 
waves passing  through  each.  Cause  the 
crystal  to  rotate  in  a  plane  parallel  with 
the  card,  and  one  of  the  holes  will  appear 
to  remain  nearly  at  rest,  while  the  other 
rotates  around  the  first.  A  ray,  PQ, 
immediately  on  entering  the  crystal  is 
divided  into  two  parts,  one  of  which,  QO, 
obeys  the  regular  law  of  refraction  ;  the  other,  QE,  does  not.  The 
former  is  called  the  ordinary  ray ;  the  latter,  the  extraordinary  ray. 
The  rays  issue  from  the  crystal  parallel  with  each  other. 

In  every  direction  in  which  one  looks  through  the 
crystal,  except  that  parallel  to  its  optical  axis,  objects  seen 
through  it  appear  double.  (See  Figure  275.)  The  optic 


Fig.  274. 


Fig.  275. 


axis  of  a  crystal  is  a  line  around  which  the  molecules 
of  the  crystal  appear  to  be  arranged  symmetrically.  A 
crystal  is  called  uniaxial  when  it  has  only  one  optic  axis, 


PRISMS    AND   LENSES.  317 

and  biaxial  when  it  has  two  such  axes.  By  far  the  largei 
number  of  crystals  of  other  substances  possess  the  prop- 
erty of  causing  objects  seen  through  them  to  appear 
double.  This  phenomenon  is  called  double  refraction. 


Section  VI. 

PRISMS   AND  LENSES. 

300.  Optical  Prisms.  —  An  optical  prism  is  a  trans- 
parent, wedge-shaped  body.      Figure    276    represents    a 
transverse  section  of  such  a  prism.      Let  AB  be  a  ray 
incident  upon  one  of  its  surfaces.     On  entering  the  prism 
it  is  refracted  toward  the  normal,  and   takes  the  direc- 
tion BC.      On  emerging  from  the  prism  it  is  again  re- 
fracted, but  now  from  the  normal  in  the  direction  CD. 
The  object  that  emits   the 

ray  will  appear  to  be  at  F. 
Observe  that  the  ray  AB, 
at  both  refractions,  is  bent 
toward  the  thicker  part,  or 
base,  of  the  prism. 

301.  Lenses.  —  Any  trans-  ms'  276' 

parent  medium  bounded  by  two  curved  surfaces,  or  by 
one  plane  and  the  other  curved,  is  a  lens. 

Experiment  211.  —  Procure  a  couple  of  lenses  thicker  in  the 
middle  than  at  the  edge  :  strong  spectacle  glasses,  or  the  large  lenses 
in  an  opera  glass  will  answer.  Hold  one  of  the  lenses  in  the  sun's 
rays,  and  notice  the  path  of  the  beam  in  dusty  air  (made  so  by  strik- 
ing together  two  blackboard  rubbers),  after  it  passes  through  the  lens  ; 


318  RADIANT  ENERGY. 

also,  that  on  a  paper  screen  all  the  rays  may  be  brought  to  a  small 
circle,  or  even  to  a  point,  not  far  from  the  lens.  This  point  is  called 
the  focus,  and  its  distance  from  the  lens,  the  focal  length  of  the 
lens. 

Find  the  focal  length  of  this  lens,  then  of  the  second,  and  then  of 
the  two  together.  You  find  the  focal  length  of  the  two  combined  is 
less  than  of  either  alone,  and  learn  that  the  more  powerful  a  lens  or 
combination  of  them  is,  the  shorter  the  focal  length ;  that  is,  the  more 
quickly  are  the  parallel  rays  that  enter  different  parts  of  the  lens 
brought  to  cross  one  another. 

Experiment  212. —  Procure  a  lens  thinner  in  the  middle  than  at 
its  edge.  One  of  the  small  lenses  or  eye-glasses  of  an  opera  glass  will 
answer.  Repeat  the  above  experiment  with  this  lens,  and  notice  that 
the  rays  emerging  from  the  lens,  instead  of  coming  to  a  point,  become 
spread  out. 

Lenses  are  of  two  classes,  converging  and  diverging, 
according  as  they  collect  rays  or  cause  them  to  diverge. 
Each  class  comprises  three  kinds  (Fig.  277)  :  — 

CLASS  I.  CLASS  H. 

1.  Double-convex     "j  Converging,  or  convex 

2.  Plano-convex         1     lenses  thicker  in 

3.  Concavo-convex.   [      the  middle  than  at 

(or  meniscus)    }     the  edges. 


4.  Double-concave     J     c'^gSe°r  ££ 

MSsaM'SiSas? 


A  straight  line,  as  AB,  normal  to  both  surfaces  of  a 
leus,  and  passing  through  its  center  of  curvature,  is  called 

its  principal  axis. 
In  every  thin  lens 
there  is  a  point  in 
the  principal  axis 
called  the  optical 
Fig.  377.  center.  Every  ray 

that  passes  through  it  has  parallel  directions  at  incidence 
and  emergence,  i.e.  can  suffer  at  most  only  a  slight  lateral 
displacement.  In  lenses  1  and  4  it  is  half-way  between 
their  respective  curved  surfaces.  A  ray,  drawn  through 


PRISMS   AND   LENSES.  319 

the  optical  center  from  any  point  of  an  object,  as  Aa 
(Fig.  286),  is  called  the  secondary  axis  of  this  point. 

3O2.  Effect  of  Lenses.  —  We  may,  for  convenience  of 
illustration,  regard  a  convex  lens  as  composed,  approxi- 
mately, of  two  prisms  placed  base  to  base,  as  A  (Fig. 
278),  and  a  concave  lens  as  composed  of  two  prisms  with 
their  edges  in  contact,  as  B.  Inasmuch  as  a  beam  ordi- 
narily strikes  a  lens  in  such  a  manner 
that  it  is  bent  toward  the  thicker  parts 
or  bases  of  these  approximate  prisms, 
it  is  obvious  that  the  lens  A  tends  to 
bend  the  transmitted  rays  toward  one 
another,  while  the  lens  B  tends  to 
separate  them.  The  general  effect  of  all  ^s-  378. 

convex  lenses  is  to  converge  transmitted  rays ;  that  of  con- 
cave lenses,  to  cause  them  to  diverge.  Incident  rays  parallel 
with  the  principal  axis  of  a  convex  lens  are  brought  to 

a  focus  F  (Fig.  279) 
at  a  point  in  the  prin- 
cipal axis.  This  point 
is  called  the  principal 
focus,  i.e.  it  is  the  focus 
of  incident  rays  par- 
allel with  the  principal 
Fig'379-  axis.  It  may  be  found 

by  holding  the  lens  so  that  the  rays  of  the  sun  may  fall 
perpendicularly  upon  it,  and  then  moving  a  sheet  of  paper 
back  and  forth  behind  it  until  the  image  of  the  sun 
formed  on  the  paper  is  brightest  and  smallest.  Or,  in  a 
room,  it  may  be  found  approximately,  by  holding  a  lens  at 
a  considerable  distance  from  a  window,  regulating  the 
distance  so  that  a  distinct  image  of  the  window  will  be 


320 


RADIANT   ENERGY. 


projected  upon  the  opposite  wall,  as  in  Figure  280.     The 
focal  length  is  the  distance  of  the  optical  center  of  the  lens 


Fig.  380. 

to  the  center  of  the  image  on  the  paper.  The  shorter 
this  distance  the  greater  is  the  power  of  the  lens. 

If  the  paper  is  kept  at  the  principal  focus  for  a  short  time, 
it  will  take  fire.  The  reason  is  apparent  why  convex  lens- 
es are  sometimes 
called  "  burning 
glasses."  A  pencil 
of  rays  emitted 
from  the  princi- 
pal focus  F  (Fig. 
279),  as  a  lumi- 
nous point,  be- 

88i.  comes  parallel  on 

emerging  from  a  convex  lens.  If  the  rays  emanate  from 
a  point  nearer  the  lens,  they  diverge  after  egress,  but  the 
divergence  is  less  than  before ;  if  from  a  point  beyond 
the  principal  focus,  the  rays  are  rendered  convergent.  A 


PRISMS   AND   LENSES. 


321 


concave  lens  causes  parallel  incident  rays  to  diverge  as 
if  they  came  from  a  point,  as  F  (Fig.  281).  This  point  is 
therefore  its  principal  focus.  It  is,  of  course,  a  virtual 
focus. 

3O3.  Conjugate  Foci.  —  When  a  luminous  point  S  (Fig. 
282)  sends 
rays  to  a  con- 
vex lens,  tho 
emerge  n  trays 
converge  to 
another  point 

S';  rays  sent  Fig.  383. 

from  S'  to  the  lens  would  converge  to  S.  Two  points 
thus  related  are  called  conjugate  foci.  The  fact  that  rays 
which  emanate  from  one  point  are  caused  by  convex 
lenses  to  collect  at  one  point,  gives  rise  to  real  images,  as 
in  the  case  of  concave  mirrors. 


Fig.  283. 


3O4.  Images  Formed. — Fairly  distinct  images  of  objects 
may  be  formed  through  very  small  apertures  (Fig.  253); 
but  owing  to  the  small  amount  of  radiant  energy  that  passes 
through  the  aperture,  the  images  are  very  deficient  in  bril- 
liancy. If  the  aperture  is  enlarged,  brilliancy  is  increased 


322  RADIANT   ENERGY. 

at  the  expense  of  distinctness.     A  convex  lens  enables  us  to 
obtain  both  brilliancy  and  distinctness  at  the  same  time. 

Experiment  213.  —  By  means  of  a  porte  lumiere  A  (Fig.  283)  in- 
troduce a  horizontal  beam  into  a  darkened  room.  In  its  path  place 
some  object,  as  B,  painted  in  transparent  colors  or 
photographed  on  glass.  (Transparent  pictures  are 
cheaply  prepared  by  photographers  for  sun-light  and 
lime-light  projections.)  Beyond  the  object  place  a 
convex  lens  L  (such  as  represented  in  Figure  283),  and 
beyond  the  lens  a  screen  S.  The  object  being  illu- 
minated by  the  beam,  all  the  rays  diverging  from 
any  point  a  are  bent  by  the  lens  so  as  to  come  to- 
gether at  the  point  a1.  In  like  manner,  all  the  rays 
proceeding  from  c  are  brought  to  the  same  point  c' ; 
and  so  also  for  all  intermediate  points.  Thus,  out  of 
Fig.  284.  fae  innumerable  rays  emanating  from  each  of  the  in- 
numerable points  on  the  object,  those  that  reach  the  lens  are  guided 
by  it,  each  to  its  own  appropriate  point  in  the  image.  It  is  evident 
that  there  must  result  an  image,  both  bright  and  distinct,  provided  the 
screen  is  suitably  placed,  i.e.  at  the  place  where  the  rays  meet.  But  if 
the  screen  is  placed  at  S'  or  S",  it  is  evident  that  a  blurred  image 
will  be  formed.  Instead  of  moving  the  screen  back  and  forth,  in  order 
to  "focus"  the  rays  properly,  it  is  customary  to  move  the  lens. 

Experiment  214. — Make  a  series  of  experiments  similar  to  those 
(Experiment  198)  with  the  concave  mirror.  Ascertain  the  focal  length 
of  the  convex  lens.  Place  the  lens  a  distance  from  a  white  wall  about 
equal  to  its  focal  length.  Place  a  candle  flame  (better  the  flame  of 
a  fish-tail  burner)  at  such  a  distance  the  other  side  of  the  lens  that  it 
will  produce  a  distinct  and  well-defined  image  on  the  wall  (Fig.  285). 

(1)  Observe  and  note  on  paper  the  size  and  kind  of  image.     Advance 
the  flame  toward  the  lens,  regulating  at  the  same  time  the  distance 
between  the  lens  and  wall,  so  as  to  preserve  a  distinctness  of  image. 

(2)  Note  the  changes  which  the  image  undergoes.     (3)  When  the 
image  and  flame  become  of  the  same  size,  measure  and  note  the  dis- 
tances of  each  from  the  lens.     (4)  Advance  the  flame  still  nearer, 
and  note  the  changes  in  the  image,  until  it  is  impossible  to  obtain  an 
image  on  the  wall.     Measure  the  distance  of  the  flame  from  the  lens, 
and  compare  this  distance  with  the  focal  length  of  the  lens.     (5)  Move 


PRISMS    AND    LENSES. 


323 


the  flame  still  nearer.     Note  whether  the  rays,  after  emerging  from 
the  lens,  are  divergent  or  convergent.    (6)  See  whether  an  image  and 


Fig.  285. 


an  object  may  change  places.  (7)  Form  images  of  the  flame  on  the 
wall  at  different  distances  from  the  lens  ;  measure  the  distances,  also 
the  linear  dimensions  (e.g.  the  width,  or  the  vertical  hight)  of  the 
images,  and  determine  whether  the  linear  dimensions  of  images  are 
proportional  to  their  distances  from  the  lens. 

305.  To  Construct  the  Image  .Formed  by  a  Convex 
Lens.  —  Given  the 
lens  L  (Fig.  286), 
whose  principal  fo- 
cus is  at  F  (or  F',  for 
rays  coming  from  the 
other  direction),  and 
object  AB  in  front  of 
it ;  any  two  of  the 
many  rays  from  A  will  determine  where  its  image  a  is  formed.  The  two 
that  can  be  traced  easily  are  the  one  along  the  secondary  axis  AOa,  and 
the  one  parallel  to  the  principal  axis  A  A':  the  latter  will  be  deviated  so 
as  to  pass  through  the  principal  focus  F,  and  will  afterward  intersect  the 
principal  axis  at  some  point  a  ;  so  this  is  the  conjugate  focus  of  A  ; 
similarly  for  B,  and  all  intermediate  points  along  the  arrow.  Thus,  a 
real  inverted  image  is  formed  at  ab. 


286. 


324 


RADIANT   ENERGY. 


3O6.  Virtual  Images  ;  Simple  Microscope.  —  Since 
rays  that  emanate  from  a  point  nearer  the  lens  than  the 
principal  focus  diverge  after  egress,  it  is  evident  that 
their  focus  must  be  virtual  and  on  the  same  side  of  the 

A' 


Fig.  287. 

lens  as  the  object.  Hence,  the  image  of  an  object  placed 
nearer  the  lens  than  the  principal  focus  is  virtual,  magnified, 
and  erect,  as  shown  in  Figure  287.  A  convex  lens  used 
in  this  manner  is  called  a  simple  microscope. 

Since  the  effect  of  concave  lenses  is  to  scatter  trans- 
mitted  rays,    pencils    of    rays    emitted   from    A   and   B 


Fig.  288. 


(Fig.  288),  after  refraction,  diverge  as  if  they  came  from 
A'  and  B',  and  the  image  will  appear  to  be  at  A'  B'. 
Hence,  images  formed  by  concave  lenses  are  virtual,  erect, 
and  smaller  than  the  object. 


PRISMS    AND    LENSES.  325 

3O7.  Spherical  Aberration.  —  In  all  ordinary  convex 
lenses  the  curved  surfaces  are  spherical,  and  the  angles 
which  incident  rays  make  with  the  little  plane  surfaces  of 
which  we  may  imagine  the  spherical  surface  to  be  made 

P. 

F' 


up,  increase  rapidly  toward  the  edge  of  the  lens.  Thus, 
while  those  rays  from  a  given  point  of  an  object,  as  A 
(Fig.  289),  which  pass  through  the  central  portion,  meet 
approximately  at  the  same  point  F,  those  which  pass 
through  the  marginal  portion  are  deviated  so  much  that 
they  cross  the  axis  at  nearer  points,  e.g.  at  F';  so  a  blurred 
image  results.  This  wandering  of  the  rays  from  a  single 
focus  is  called  spherical  aberration.  The.  evil  may  be 
largely  corrected1  by  interposing  a  diaphragm  DD',  pro- 
vided with  a  central  aperture,  smaller  than  the  lens,  so  as 
to  obstruct  those  rays  that  pass  through  the  marginal  part 
of  the  lens. 

Experiment  215.  —  (Illustrating  spherical  aberration.)  Cut  a 
cardboard  disk  as  large  as  the  convex  lens  (Fig.  284).  Cut  a  ring 
of  holes  near  the  circumference,  and  also  a  ring  near  the  center. 
Support  the  disk  close  to  the  lens,  so  as  to  cover  one  of  its  surfaces. 
Place  the  whole  in  a  beam  from  a  porte  lumiere.  Catch  refracted 
beams  on  a  screen.  Move  the  screen  away  from  the  lens.  The  beams 
through  the  outer  ring  of  spots  are  the  first  to  cross  one  another  and 
form  an  image.  Further  away,  the  inner  beams  coincide,  forming 
an  image.  The  outer  ones,  having  crossed,  form  a  ring  of  spots. 

1  It  can  be  wholly  corrected  only  by  modifying  the  curvature  of  the  surfaces  of 
the  lens.  A  lens  having  surfaces  thus  modified  is  said  to  be  aplanatic. 


326 


RADIANT   ENERGY. 


Section  VII. 

PRISMATIC   ANALYSIS   OF   LIGHT- WAVES. — SPECTRA. 

3O8.  Analysis  of  Light-Waves  which  Produce  the 
Sensation  of  White. 

Experiment  216.  —  Place  the  disk  with  adjustable  slit  in  the  aper- 
ture of  a  porte  lumiere,  so  as  to  exclude  all  light-waves  from  a  darkened 
room  except  those  which  pass  through  the  slit.  Near  the  slit  inter- 
pose a  double-convex  lens  of  (say)  10-inch  focus.  A  narrow  sheet  of 
light  will  traverse  the  room  and  produce  an  image  AB  (Fig.  290)  of 
the  slit  on  a  white  screen  placed  in  its  path.  Now  place  a  glass  prism 
C  in  the  path  of  the  narrow  sheet  of  light-waves  and  near  to  the  lens 
with  its  edge  vertical.  (1)  The  light-waves  now  are  not  only  turned 


Fig.  290. 


from  their  former. path,  but  that  which  before  was  a  narrow  sheet,  is, 
after  emerging  from  the  prism,  spread  out  fan-like  into  a  wedge-shaped 
body,  with  its  thickest  part  resting  on  the  screen.  (2)  The  image, 
before  only  a  narrow,  vertical  band,  is  now  drawn  out  into  a  long 


PRISMATIC    ANALYSIS   OF   LIGHT-WAVES.  327 

horizontal  ribbon,  DE.  (3)  The  image,  before  white,  now  presents  all 
the  colors  of  the  rainbow,  from  red  at  one  end  to  violet  at  the  other ; 
it  passes  gradually  through  all  the  gradations  of  red,  orange,  yellow, 
green,  blue,  and  violet.  (The  difference  in  deviation  between  the  red 
and  the  violet  is  purposely  much  exaggerated  in  the  figure.) 

From  this  experiment  we  learn  (1)  that  white  waves  (i.e. 
those  waves  which  are  capable  of  producing  the  sensation 
of  white)  are  not  simple  in  their  composition,  but  the  result 
of  a  mixture.  (2)  The  color  waves  of  which  white  waves  are 
composed  may  be  separated  by  refraction.  (3)  The  cause  of 
the  separation  is  due  to  the  different  degrees  of  deviation 
which  they  undergo  by  refraction.  Red  waves,  which  are 
always  least  turned  aside  from  a  straight  path,  are  the 
least  refrangible.  Then  follow  orange,  yellow,  green,  blue, 
and  violet  in  the  order  of  their  refrangibility.  The  many- 
colored  ribbon  DE  is  called  the  solar  spectrum.  This 
separation  of  white  waves  into  their  constituents  is  called 
dispersion.  The  variety  of  color  waves  of  which  white 
waves  are  composed  is  really  infinite ;  but  we  name  the 
seven  principal  ones  as  follows:  red,  orange  (or  citron), 
yellow,  green,  cyan-blue,  ultramarine-blue,  and  violet;  these 
are  called  the  prismatic  colors.  The  names  of  the  blues 
are  derived  from  the  names  of  the  pigments  which  most 
closely  resemble  them. 

3O9.  The  Kainbow. — The  rainbow  is  an  illustration  of  a  solar 
spectrum  on  a  grand  scale.  It  is  the  result  of  refraction,  reflection,  and  dis- 
persion of  sunlight  by  falling  raindrops.  Let  spheres  1  and  2  (Fig.  291) 
represent  drops  at  the  extreme  opposite  edges  of  the  bow.  The  eye  is  in  a 
position  to  receive  after  the  dispersion  and  internal  reflection  of  the  light- 
waves within  1  drop,  only  the  red  waves ;  consequently  this  part  of  the 
bow  appears  red.  So,  likewise,  from  drop  2,  the  eye  receives  only  violet ; 
consequently  this  edge  appears  violet.  In  like  manner,  the  intermediate 
colors  of  the  bow  are  sifted  out. 

Outside  the  primary  bow  a  secondary  bow  (Fig.  292)  is  sometimes  seen. 
Drops  3  and  4  (Fig.  291)  are  supposed  to  be  at  the  opposite  edges  of  the 


328 


RADIANT  ENERGY. 


Fig.  291. 

secondary  bow.  It  will  be  seen  that  the  light-waves  undergo  two  internal 
reflections  within  the  drops  which  produce  this  bow.  The  colors  of  this 
bow  are  in  reverse  order  of  those  of  the  primary  bow,  and  less  brilliant. 


Fig.  393. 

31O.  Synthesis  of  White  Waves. — The  composition 
of  white  waves  has  been  ascertained  by  the  process  of  anal- 
ysis ;  can  it  be  verified  by  synthesis  ?  —  i.e.  can  the  colors 


PRISMATIC   ANALYSIS   OF   LIGHT-WAVES.  329 

after  dispersion  be  reunited  ?  and,  if  so,  will  white  be  re- 
stored ? 

Experiment  217. — Place  a  second  prism  (2)  in  such  a  position 
(Z^7)  that  light-waves  which  have  passed  through  one  prism  (1),  and 
been  refracted  and  decomposed,  may  be  refracted  back,  and  the  colors 
will  be  reblended,  and  a  white  image  of  the  slit  will  be  restored  on 
the  screen. 

Experiment  218.  —  Place  a  large  convex  lens,  or  a  concave  mirror, 
so  as  to  receive  the  colors  after  dispersion  by  a  prism,  and  bring  the  rays 
to  a  focus  on  a  screen.  The  image  produced  will  be  white. 

311.  Cause  of  Color  Revealed  by  Dispersion.  —  Color 
is  determined  solely  by  the  number  of  waves  emitted  by  a 
luminous  body  in  a  second  of  time,  or  by  the  corresponding 
wave-length.  In  a  dense  medium,  the  short  waves  are  more 
retarded  than  the  longer  ones ;  hence  they  are  more  re- 
fracted. This  is  the  cause  of  dispersion.  The  ether  waves 
diminish  in  length  from  the  red  to  the  violet.  As  pitch 
depends  on  the  number  of  aerial  waves  which  strike  the 
ear  in  a  second,  so  color  depends  on  the  number  of  ethereal 
waves  which  strike  the  eye  in  a  second. 

From  well-established  data,  determined  by  a  variety  of  methods  (see 
larger  works),  physicists  have  calculated  the  number  of  waves  that  suc- 
ceed one  another  for  each  of  the  several  prismatic  colors,  and  the  corre- 
sponding wave-lengths ;  the  following  table  contains  the  results.  The  let- 
ters A,  C,  D,  etc.,  refer  to  Fraunhofer's  lines  (see  Plate  I.). 

Length  of  waves  Number  of  waves 

in  millimeters.  per  second. 

Dark  red A 000760 395,000,000,000,000 

Orange C 000656 458,000,000,000,000 

Yellow D 000589 510,000,000,000,000 

Green E 000527 570,000,000,000,000 

C.  Blue F 000486 618,000,000,000,000 

U.  Blue G 000431 697,000,000,000,000 

Violet H 000397 760,000,000,000,000 

There  is  a  limit  to  the  sensibility  of  the  eye  as  well  as  of  the  ear.  The 
limit  in  the  number  of  vibrations  appreciable  by  the  eye  lies  approximately 


330  KADIANT   ENERGY, 

within  the  range  of  numbers  given  in  the  above  table ;  i.e.  if  the  succes- 
sion of  waves  is  much  more  or  less  rapid  than  indicated  by  these  numbers, 
they  do  not  produce  the  sensation  of  sight. 

312.  Continuous    Spectra.  —  All  luminous  solids  and 
liquids   give  continuous  spectra.      If  the  spectrum  is   not 
complete,  as  when  the  temperature  is  too  low,  it  will  begin 
with  red,  and  be  continuous  as  far  as  it  goes. 

313.  Spectroscope. —  A  small  instrument  called  a  pocket  spectro- 
scope l  will  answer  for  all  experiments  given  in  this  book.     More  elaborate 
experiments  require   more   elaborate   apparatus,  a  description  of  which 
must  be  sought  for  in  larger  works  on  this  subject.     This  instrument  con- 
tains three  or  more  prisms,  A,  B,  and  C  (Fig.  293).    The  prisms  are  en- 
closed in  a  brass  tube  D,  and  this  tube  in  another  tube  E.     F  is  a  convex 
lens,  and  G  is  an  adjustable  slit.     By  moving  the  inner  tube  back  and 
forth,  the  instrument  may  be  so  focused  that  parallel  rays  will  fall  upon 


Fig.  393. 

prism  A.  By  varying  the  kind  of  glass  used  in  the  different  prisms,2  as 
well  as  their  structure,  the  deviation  of  light-waves  from  a  straight  path, 
in  passing  through  them,  is  overcome,  while  the  dispersion  is  preserved. 
On  account  of  the  directness  of  the  path  of  light-waves  through  it,  this 
instrument  is  called  a  direct-vision  spectroscope. 

314.   Bright  Line,  Absorption,  or  Reversed  Spectra. 

Experiment  258.  —  Open  the  slit  about  one-sixteenth  of  an  inch 
wide,  by  turning  the  milled  ring  M  (Fig. 
294),  and  look  through  the  spectroscope  at 
the  sky  (not  at  the  sun,  for  its  light-waves 
are  too  intense  for  the  eye),  and  you  will  see 
a  continuous  spectrum. 

1It  is  expected  that  the  pupil  will  be  provided  with  a  pocket  spectroscope,  the  cost  of 
which  need  not  exceed  ten  dollars. 

2  A  and  C  are  crown-glass,  and  B  is  flint-glass. 


PRISMATIC    ANALYSIS   OF   LIGHT- WAVES.  331 

Experiment  219. —  Repeat  the  last  experiment  with  a  candle, 
kerosene,  or  ordinary  gas  flame,  and  you  will  obtain  similar  results. 

Experiment  220. —  Take  a  piece  of  platinum  wire  16  inches  long. 
Seal  one  end  by  fusion  to  a  short  glass  tube  for  a  handle.  Bend  the 
wire  at  a  right  angle.  Dip  a  portion  of  the  wire  into  a  strong  solution 
of  common  salt,  and  support  it  by  a  clamp  in  the  midst  of  the  almost 
invisible  and  colorless  flame  of  a  Bunsen  burner  or 
alcohol  lamp  (Fig.  295).  Instantly  the  flame  becomes 
luminous  and  colored  a  deep  yellow.  Examine  it  with 
a  spectroscope,  and  you  will  find,  instead  of  a  continuous 
spectrum  beginning  with  red,  only  a  bright,  narrow 
line  of  yellow,  in  the  yellow  part  of  the  spectrum,  next 
the  orange.  Your  spectrum  consists  essentially  of  a 
single  bright  yellow  line  on  a  comparatively  dark 
ground  (see  Sodium,  Plate  L,  frontispiece). 

Experiment  221.  —  Heat  the  platinum  wire  until  it  ceases  to  color 
the  flame,  then  dip  it  into  a  solution  of  chloride  of  lithium,  and  repeat 
the  last  experiment.  You  obtain  a  carmine-tinted  flame,  and  see 
through  the  spectroscope  a  bright  red  line  and  a  faint  orange  line 
(see  Lithium,  Plate  I.). 

Experiment  222.  —  Use  potassium  hydrate,  and  you  obtain  a 
violet-colored  flame,  and  a  spectrum  consisting  of  a  red  line  and  a 
violet  line  (the  latter  is  very  difficult  to  see  even  with  the  best  instru- 
ments). Use  strontium  nitrate,  and  obtain  a  crimson  flame,  and  a 
spectrum  consisting  of  several  lines  in  the  red  and  the  orange,  and  a 
blue  line  (see  Potassium  and  Strontium,  Plate  L). 

Experiment  223.  —  Use  a  mixture  of  several  of  the  above  chemi- 
cals, and  you  will  obtain  a  spectrum  containing  all  the  lines  that  char- 
acterize the  several  substances. 

Every  chemical  compound  used  in  the  above  experiments 
contains  a  different  metal,  e.g.  common  salt  contains  the 
metal  sodium ;  the  other  substances  used  successively  con- 
tain respectively  the  metals  lithium,  potassium,  and  stron- 
tium. These  metals,  when  introduced  into  the  flame,  are 
vaporized,  and  we  get  their  spectra  when  in  a  gaseous 
state.  All  incandescent  gases,  unless  under  great  pressure, 
give  discontinuous,  or  bright  line,  spectra,  and  no  two  gases 
give  the  same  spectra. 


332  RADIANT   ENERGY. 

315.    Dark-line  Spectra. 

Experiment  224.  —  Close  the  slit  of  the  spectroscope  so  that  the 
aperture  will  be  very  narrow;  direct  it  once  more  to  the  sky,  and 
slowly  move  the  inner  tube  back  and  forth,  and  you  will  find,  with  a 
certain  suitable  adjustment  which  may  be  obtained  by  patient  trial, 
that  the  solar  spectrum  is  not  in  reality  continuous,  but  is  crossed  by 
several  dark  lines  (see  Solar  Spectrum,  Plate  I.). 

Remark.  —  In  general  it  is  best  to  focus  either  the  D  line  in  the  orange, 
or  the  E  line  in  the  green.  The  inner  sliding  tube  ought  to  be  drawn  out 
a  little  when  examining  the  blue  end  of  the  spectrum,  and  pushed  in  for 
focusing  the  lines  in  the  red. 

Experiment  225.  —  Put  a  few  copper  turnings  in  a  test-tube,  add 
a  little  nitric  acid.  Hold  the  tube  causing  the  colored  vapor  before 
the  slit,  and  notice  the  black  bands. 

Experiment  226.  —  The  electric  light  is  now  in  so  common  use 
that  it  may  be  possible  to  perform  this  experiment.  Between  the 
electric  light  and  the  spectroscope  introduce  the  flame  of  a  Bunsen 
burner,  and  color  it  yellow  with  salt.  Examine  the  spectrum  formed 
through  this  yellow  flame. 

In  the  last  experiment  you  would  naturally  expect  to 
find  the  yellow  part  of  the  spectrum  uncommonly  bright, 
for  there  would  apparently  be  added  to  the  yellow  waves 
of  the  electric  light  the  yellow  waves  of  the  salted  flame. 
But  precisely  where  you  would  look  for  the  brightest 
yellow,  there  you  discover  that  the  spectrum  is  crossed 
by  a  dark  line.  If  you  use  salts  of  lithium,  potassium, 
and  strontium  in  a  similar  manner,  you  will  find  in  every 
case  your  spectrum  crossed  by  dark  lines  where  you  would 
expect  to  find  bright  lines.  Remove  the  Bunsen  flame, 
and  the  dark  lines  disappear.  It  thus  appears  that  the 
vapors  of  different  substances  absorb  or  quench  the  very 
same  waves  that  they  are  capable  of  emitting ;  very  much, 
it  would  seem,  as  a  given  tuning-fork  selects  from  various 
sound-waves  only  those  of  a  definite  length  corresponding 


PRISMATIC   ANALYSIS  OF  LIGHT-WAVES.  333 

to  its  own  vibration-period.  The  dark  places  of  the  spec- 
trum are  illuminated  by  the  salted  flame ;  but  these  places 
are  so  feebly  illuminated  in  comparison  with  those  places 
illuminated  by  the  electric  light,  that  the  former  appear 
dark  by  contrast.  Light-waves  transmitted  through  cer- 
tain liquids  (as  sulphate  of  quinine  and  blood)  and  certain 
solids  (as  some  colored  glasses)  produce  dark-line  spectra. 
These  spectra  are  obtained  only  when  light-waves  pass 
through  media  capable  of  absorbing  waves  of  certain 
length;  hence  they  are  commonly  called  absorption  spec- 
tra. Since  a  given  vapor  causes  dark  lines  precisely  where, 
if  it  were  itself  the  only  radiator  of  light-waves,  it  would 
cause  bright  lines,  dark-line  spectra  are  frequently  called 
reversed  spectra.  There  are  then  three  kinds  of  spectra: 
continuous  spectra,  produced  by  luminous  solids,  liquids, 
or,  as  has  been  found  in  a  few  instances,  gases  under  great 
pressure;  bright-line  spectra,  produced  by  luminous  vapors; 
and  absorption  spectra,  produced  by  light-waves  that  have 
been  sifted  by  certain  media. 

316.  Spectrum  Analysis.  —  More  elaborate  spectroscopes  contain 
many  prisms,  by  which  the  purity  of  the  spectrum  is  greatly  increased. 
(By  purity  is  meant  a  freedom  from  the  overlapping  of  images  of  the  slit, 
by  which  many  lines  of  the  spectrum  are  obscured.)  They  also  contain  an 
illuminated  scale  which  may  be  seen  adjacent  to  the  spectrum,  by  which  the 
exact  position  of  the  lines  and  their  relative  distances  from  one  another 
can  be  accurately  determined,  and  a  telescope  by  which  the  spectrum  and 
scale  may  be  magnified.  The  positions  of  some  of  the  prominent  lines  of 
the  solar  spectrum  were  first  determined,  mapped,  and  distinguished  from 
one  another  by  certain  letters  of  the  alphabet,  by  Fraunhofer;  hence  the 
dark  linos  of  the  solar  spectrum  are  commonly  called  Fraunhofer's  lines. 
So  far  as  discovered,  no  two  substances  have  a  spectrum  consisting  of  the 
same  combination  of  lines  ;  and,  in  general,  different  substances  but  very 
rarely  possess  lines  appearing  to  be  common  to  both.  Hence,  when  we  have 
once  observed  and  mapped  the  spectrum  of  any  substance,  we  may  ever 
after  be  able  to  recognize  the  presence  of  that  substance  when  emitting 
light-waves,  whether  it  is  in  our  laboratory  or  in  a  distant  heavenly  body. 


334  RADIANT  ENEKGY. 

The  spectroscope,  therefore,  furnishes  us  a  most  efficient  means  of  detect- 
ing the  presence  (or  absence)  of  any  elementary  substance,  even  when 
it  is  combined  or  mixed  with  other  substances.  It  is  not  necessary  that 
the  given  substance  should  exist  in  large  quantities;  for  example,  a 
fourteen-millionth  of  a  milligram  of  sodium  can  be  detected  by  the  spec- 
troscope. 

317.  Celestial  Chemistry  and  Physics.  —  The  spectrum  of 
iron  has  been  mapped  to  the  extent  of  460  bright  lines.     The  solar  spec- 
trum furnishes  dark  lines  corresponding  to  nearly  all  these  bright  lines. 
Can  there  be  any  doubt  of  the  existence  of  iron  in  the  sun  ?     By  exami- 
nation of  the  reversed  spectrum   of  the   sun,  we   are  able  to  determine 
with    certainty   the    existence    there  of    sodium,  calcium,  coppery    zinc, 
magnesium,  hydrogen,  and   many  other  known  substances.      The  moon 
and  other  heavenly  bodies  that  are  visible  only  by  reflected  sunlight  give 
the  same  spectra  as  the  sun,  while  those  that  are  self-luminous  give  spectra 
which  differ  from  the  solar  spectrum. 

318.  Relative    Heating-    and    Chemical    Effects    of 
Ether- Waves  of  Different  Lengths.  —  If  a  sensitive  thermome- 
ter is  placed  in  different  parts  of  the  solar  spectrum,  it  will  indicate  heat  in 
all  parts ;  but  the  heat  generally  increases  from  the  violet  toward  the  red. 
It  does  not  cease,  however,  with  the  limit  of  the  visible  spectrum ;  indeed, 
if  the  prism  is  made  of  flint  glass,  the  greatest  heat  is  just  beyond  the  red. 
A  strip  of  paper  wet  with  a  solution  of  chloride  of  silver  suffers  no  change  in 
the  dark  ;  in  the  light-waves  it  quickly  turns  black ;  exposed  to  the  light- 
waves of  the  solar  spectrum,  it  turns  dark,  but  quite  unevenly.    The  change 
is  slowest  in  the  red,  and  constantly  increases,  till  about  the  region  indicated 
by  G  (see  Solar  Spectrum,  Plate  I.),  where  it  attains  its  maximum ;  from 
this  point  it  falls  off,  and  ceases  at  a  point  considerably  beyond  the  limit  of 
the  violet.     It  thus  appears  that  the  solar  spectrum  is  not  limited  to  the 
visible  spectrum,  but  extends  beyond  at  each  extremity.     Those  waves 
that  are  beyond  the  red  are  usually  called  the  infra-red  waves,  while  those 
that  are  beyond  the  violet  are  called  the  ultra-violet  waves.     The  infra-red 
waves  are  of  longer  vibration-period,  and  the  ultra-violet  of  shorter  period, 
than  the  light-waves. 

319.  Only  one  Kind  of  Kadiation.  —  The  fact  that  radiant 
energy  produces  three  distinct  effects  —  viz.   luminous,   heating,  and 
chemical  —  formerly  gave  rise  to  a  prevalent  idea  that  there  are  three 
distinct  kinds  of  radiation.     There  is,  however,  absolutely  no  proof  that 
these  different  effects  are  produced  by  different  kinds  of   radiation, 


PRISMATIC    ANALYSIS    OF    LIGHT-WAVES.  335 

Science  recognizes  in  radiations  no  distinctions  but  periods,  wave  lengths, 
and  wave  forms.  The  same  radiation  that  produces  vision  can  generate 
heat  and  chemical  action.  The  fact  that  the  infra-red  and  ultra-violet 
rays  do  not  affect  the  eye  does  not  argue  that  they  are  of  a  different 
nature  from  those  that  do,  but  it  does  show  that  there  is  a  limit  to  the 
susceptibility  of  the  eye  to  receive  impressions  from  radiation.  Just  as 
there  are  sound-waves  of  too  long,  and  others  of  too  short  period  to  affect 
the  ear,  so  there  are  ethereal  waves,  some  of  too  long,  and  others  of  too 
short  period  to  affect  the  eye. 

While  waves  traverse  the  ether  there  is  neither  heat  nor  light  (i.e. 
sensation)  ;  hence  the  propriety  of  applying  either  of  these  terms  to  a 
train  of  waves  traversing  the  ether  may  well  be  called  in  question.  Yet 
this  is  all  that  traverses  the  space  between  the  sun  and  the  earth. 

32O.  Chromatic  Aberration.  —  There  is  a  serious  de- 
fect in  ordinary  convex  lenses,  to  which  we  have  not  before 
alluded,  called  chromatic  aberration,  which  has  required 
the  highest  skill  to  correct.  The  convex  lens  both 
refracts  and  disperses  the  light-waves  that  pass  through  it. 
The  tendency,  of  course,  is  to  bring  the  more  refrangible 
rays,  as  the  violet,  to  a  focus  much  sooner  than  the  less 
refrangible  rays,  such  as  the  red.  The  result  is  a  disagree- 
able coloration  of  the  images  that  are  formed  by  the  lens, 
especially  by  that  portion  of  the  light-waves  that  passes 
through  the  lens  near  its  edges.  This  evil  has 
been  overcome  very  effectually  by  combining  with 
the  convex  lens  a  plano-concave  lens.  Now,  if  a 
crown-glass  convex  lens  is  taken,  a  flint-glass 
concave  lens  may  be  prepared  that*  will  correct  the 
dispersion  of  the  former  without  neutralizing  all  Flgt  396' 
its  refraction.1  A  compound  lens,  composed  of  these  two 
lenses  (Fig.  296)  cemented  together,  constitutes  what  is 
called  an  achromatic  lens. 

1  The  refractive  and  dispersive  powers  of  the  two  lenses  are  not  proportional. 


336  RADIANT   ENERGY. 

Section   VIII. 

COLOR. 

321.  Color  by  Absorption.  —  Color  is  a  sensation  ;  it 
has  no  material  existence.  The  term  "yellow  light" 
means,  primarily,  a  particular  sensation  ;  secondarily,  it 
means  the  physical  cause  of  this  sensation,  i.e.  a  train  of 
ether-waves  of  a  particular  frequency.  "  All  objects  are 
black  in  the  dark";  this  is  equivalent  to  saying  that 
without  light  there  is  no  color. 

Experiment  227.  —  By  means  of  a  porte  lumiere  introduce  a  beam 
of  sunlight  into  a  dark  room.  With  the  slit  and  prism  form  a  solar 
spectrum.  Between  the  slit  and  prism  introduce  a  deep  red  glass  ; 
all  the  colors  of  the  spectrum  except  the  red  are  much  reduced  in 
intensity. 

It  thus  appears  that  the  color  of  a  colored  transparent 
object,  as  seen  by  transmitted  light,  arises  from  the 
unequal  absorption  of  the  different  colors  of  white  light 
incident  upon  it.  A  red  glass  absorbs  less  red  light  than 
light  of  other  colors.  The  color  produced  by  absorption 
is  rarely  very  pure,  the  particular  hue  of  the  transmitted 
light  being  due  merely  to  a  predominance  of  certain  colors, 
and  not  to  the  absence  of  all  others.  As  the  absorbing 
layer  is  thicker,  the  resulting  color  is  purer  but  less 
intense. 

Experiment  228.  —  We  have  found  that  common  salt  introduced 
into  a  Bunsen  flame  renders  it  luminous,  and  that  the  light  when 
analyzed  with  a  prism  is  found  to  contain  only  yellow.  Expose 
papers  or  fabrics  of  various  colors  to  this  light  in  a  darkened  room. 
JVo  one  of  them  except  yellow  exhibits  its  natural  color. 


COLOR. 


337 


Experiment  229.  —  Hold  a  narrow  strip  of  red  paper  or  ribbon  in 
the  red  portion  of  the  solar  spectrum  ;  it  appears  red.  Slowly  move 
it  toward  the  other  end  of  the  spectrum  ;  on  leaving  the  red  it 
becomes  darker,  and  when  it  reaches  the  green  it  is  quite  black  or 
colorless,  and  remains  so  as  it  passes  the  other  colors  of  the  spectrum. 
Repeat  the  experiment,  using  other  colors,  and  notice  that  only  in 
light  of  its  own  color  does  each  strip  of  paper  appear  of  its  natural 
color,  while  in  all  other  colors  it  is  dark. 

These  experiments  show  that  the  color  of  a  body  seen  by 
light  reflected  from  it  depends  both  upon  the  color  of  the 
light  incident  upon  it  and  upon  the  nature  of  the  body. 

If  a  piece  of  colored  glass,  A  B  (Fig.  297),  be  held  near  a  window  so 
as  to  receive,  obliquely,  rays  of  sunlight,  a  portion  of  the  light  will  be 
reflected  by  the  anterior  surface  of  the  glass,  and,  falling  upon  the  white 
ceiling,  will  illuminate 
it  with  white  light. 
Another  portion  of  the 
light  will  enter  the 
glass  and  be  reflected 
from  the  posterior  sur- 
face ;  this  light,  having 
entered  the  glass  and 
traveled  in  it  a  distance 
a  little  greater  than 
twice  its  thickness,  will  suffer  an  unequal  absorption  of  its  rays,  and 
after  emerging  from  the  glass  will,  if  the  glass  be  blue,  illuminate  a 
neighboring  portion  of  the  ceiling  with  blue  light.  This  illustrates  the 
method  by  which  pigments  afford  color.  Thus,  the  first  surface  of  a 
water-color  drawing  reflects  the  white  daylight.  Most  of  the  light 
reflected  to  the  eye  has,  however,  passed  through  the  pigment  to  the 
white  paper  beneath,  and  being  reflected  from  this,  again  passes  through 
the  layer  of  pigment  before  reaching  the  eye.  With  less  transparent 
pigments  the  light  may  be  reflected  merely  by  particles  of  pigment 
beneath  the  surface.  The  color  of  paints  and  pigments  is,  therefore,  due 
to  the  rays  which  they  absorb  least  readily.  When  we  paint  our  houses 
we  do  not  apply  color  to  them  ;  we  apply  substances  which  have  the 
property  of  absorbing  or  subtracting  from  white  light  largely  all  the 


Fig.  297. 


338  RADIANT   ENERGY, 

colors  except  those  which  we  would  have  our  houses  appear.     This  is 
technically  called  selective  absorption. 

The  color  of  bodies  thus  depends  generally  upon  their  molecular 
structure.  Different  bodies  quench  different  portions  of  the  complex 
sunlight.  The  unquenched  light  determines  the  color  of  a  body. 

322.  Mixing-  Colors.  —  A  mixture  of  all  the  prismatic 
colors  in  the  proportion  found  in  sunlight  produces  white. 
Can  white  be  produced  in  any  other  way  ? 

Experiment  230.  —  On  a  black  surface,  A  (Fig.  298),  lay  two 
small  rectangular  pieces  of  paper,  one  yellow  and  the  other  blue, 
about  two  inches  apart.  In  a  vertical  position 
between  these  papers,  and  from  3  inches  to  6  inches 
above  them,  hold  a  slip  of  plate  glass,  C.  Looking 
obliquely  down  through  the  glass  you  may  see  the 
blue  paper  by  transmitted  light-waves  and  the 
yellow  paper  by  reflection.  That  is,  you  see  the 
object  itself  in  the  former  case,  and  the  image  of 
the  object  in  the  latter  case.  By  a  little  manipula- 
tion  the  image  and  the  object  may  be  made  to 
overlap  each  other,  when  both  colors  will  apparently 
Fig.  398.  disappear,  and  in  their  place  the  color  which  is 
the  result  of  the  mixture  will  appear.  In  this  case  it  will  be  white, 
or  rather,  gray,  which  is  white  of  a  low  degree  of  luminosity.  If  the 
color  be  yellowish,  lower  the  glass  ;  if  bluish,  raise  it. 

Experiment  231.  —  With  the  rotating  apparatus,  rotate  the  disk 
(Fig.  299)  which  contains  only  yellow  and  blue.  The  colors  (i.e.  the 
sensations)  so  blend  in  the  eye  as  to  produce  the  sensation  of  gray. 


X 


Fig.  399.  Fig.  30O.  Fig.  3O1. 


COLOR.  339 

Figure  300  represents  "  Newton's  disk,"  which  contains 
the  seven  prismatic  colors  arranged  in  a  proper  proportion 
to  produce  gray  when  rotated. 

In  like  manner,  you  may  produce  white  by  mixing 
purple  and  green  ;  or,  if  any  color  on  the  circumference 
of  the  circle  (see  Complementary  Colors,  Plate  I)  be  mixed 
with  the  color  exactly  opposite,  the  resulting  color  will  be 
gray.  Green  mixed  with  red,  in  varying  proportions,  will 
produce  any  of  the  colors  in  a  straight  line  between  these 
two  colors  in  the  diagram  (Plate  I),  green  mixed  with 
violet  will  produce  any  of  the  colors  between  them ;  and 
violet  mixed  with  red  gives  purple.  The  three  colors,  red, 
green,  and  violet,  mixed  (Fig.  301),  give  gray  (see  §  324). 

All  colors  are  represented  in  the  spectrum,  except  the  purple  hues. 
The  latter  form  the  connecting  link  between  the  two  ends  of  the 
spectrum.  Our  color  chart  (Plate  I)  is  intended  to  represent  the  sum 
total  of  all  the  sensations  of  color.  By  means  of  this  chart  we  may 
determine  the  result  of  the  (optical)  mixture  of  any  two  colors,  as 
follows  :  Find  the  places  occupied  upon  the  chart  by  the  two  colors 
which  are  to  be  mixed,  and  unite  the  two  points  by  a  straight  line.  The 
color  produced  by  the  mixture  will  invariably  be  found  at  the  center  of 
this  line. 

323.    Mixing-  Pigments. 

Experiment  232.  —  Mix  a  little  of  the  two  pigments,  chrome 
yellow  and  ultramarine  blue,  and  you  obtain  a  green  pigment. 

The  last  three  experiments  show  that  mixing  certain 
colors,  and  mixing  pigments  of  the  same  name,  may  pro- 
duce very  different  results.  In  the  first  experiments  you 
mixed  colors  ;  in  the  last  experiment  you  did  not  mix 
colors,  and  we  must  seek  an  explanation  of  the  result 
obtained.  If  a  glass  vessel  with  parallel  sides  containing 
a  blue  solution  of  sulphate  of  copper  be  interposed  in  the 


340  RADIANT   ENERGY. 

path  of  the  lightwaves  which  form  a  solar  spectrum,  it 
will  be  found  that  the  red,  orange,  and  yellow  waves  are 
cut  out  of  the  spectrum,  i.e.  the  liquid  absorbs  these 
waves.  And  if  a  yellow  solution  of  bichromate  of  potash 
or  picric  acid  be  interposed,  the  blue  and  violet  waves  will 
be  absorbed.  It  is  evident  that,  if  both  solutions  be  inter- 
posed, all  the  colors  will  be  destroyed  except  the  green, 
which  alone  will  be  transmitted  ;  thus  :  — 


Cancelled  by  the  blue  solution,  $  0  ^  G  B  V. 

Cancelled  by  the  yellow  solution,  R  O  Y  G 

Cancelled  by  both  solutions,  $  0  V  G 


In  a  similar  manner,  when  white  light  strikes  a  mixture  of  yellow  and 
blue  pigments  on  the  palette,  it  penetrates  to  some  depth  into  the 
mixture  ;  and,  during  its  passage  in  and  out,  all  the  colors  except  the 
green  are  destroyed  ;  so  the  mixed  pigments  necessarily  appear  green. 
But  when  a  mixture  of  yellow  and  blue  waves  enters  the  eye,  we  get,  as 
the  result  of  the  combined  sensations  produced  by  the  two  colors,  the 
sensation  of  white  ;  hence  a  mixture  of  yellow  and  blue  gives  white. 

The  color  square  3  (Plate  I)  represents  the  result  of  the  mixture  of 
pigments  1  and  2  ;  while  4  represents  the  result  of  the  optical  mixture  of 
the  same  colors. 

324.  Theory  of  Color  Vision.  —  The   generally   accepted 
theory  of  color  vision  is  that  of  Dr.  Young  (1801-2),  verified  by  Maxwell 
and  Helmholtz.     It  supposes  the  existence  of  three  color  sensations,  red, 
green,  and  violet.     These  excited  simultaneously,  and  with  proper  inten- 
sities, produce  the  sensation  of  white  light.     Combined  in  twos,  they 
produce  the  remaining  color  sensations.     Thus  red  and  green  sensations 
combined  give  yellow  or  orange  ;  green  and  violet  give  blue,  etc.     The 
longer  light-  waves  excite  the  sensation  of  red  ;  together  with  those  some- 
what shorter,  they  excite  both  red  and  green,  thus  giving  yellow,  and  so 
on.     Strictly  speaking,  light-waves  of  any  length  excite  all  three  sen- 
sations ;  but  usually  either  one  or  two  of  them  greatly  predominate. 

325.  Complementary  Colors. 

Experiment  233.  —  On  a  piece  of  gray  paper  lay  a  circular  piece 
of  blue  paper  15  mm  in  diameter.  Attach  one  end  of  a  piece  of 


COLOR.  341 

thread  to  the  colored  paper,  and  hold  the  other  end  in  the  hand. 
Place  the  eyes  within  about  15  cm  of  the  colored  paper,  and  look 
steadily  at  the  center  of  the  paper  for  about  fifteen  seconds  ;  then, 
without  moving  the  eyes,  suddenly  pull  the  colored  paper  away,  and 
instantly  there  will  appear  on  the  gray  paper  an  image  of  the  colored 
paper,  but  the  image  will  appear  to  be  yellow.  This  is  usually  called 
an  after-image.  If  yellow  paper  be  used,  the  color  of  the  after-image 
will  be  blue  ;  and  if  any  other  color  given  in  the  diagram  (Plate  I.), 
the  color  of  its  after-image  will  be  the  color  that  stands  opposite  to  it. 

This  phenomenon  is  explained  as  follows  :  When  we 
look  steadily  at  blue  for  a  time,  the  eyes  become  fatigued 
by  this  color,  and  less  susceptible  to  its  influence,  while 
they  are  fully  susceptible  to  the  influence  of  other  colors ; 
so  that  when  they  are  suddenly  brought  to  look  at  white, 
which  may  be  regarded  as  a  compound  of  yellow  and  blue, 
they  receive  a  vivid  impression  from  the  former,  and  a 
feeble  impression  from  the  latter ;  hence  the  predominant 
sensation  is  yellow.  Any  two  colors  which  together  pro- 
duce white  are  said  to  be  complementary  to  each  other. 
The  opposite  colors  in  the  diagram  (Plate  I.)  are  comple- 
mentary to  one  another. 

The  complement  of  green  is  purple,  a  compound  color 
not  existing  in  the  spectrum. 

326.  Effect  of  Contrast.  —  When  different  colors  are  seen  at 
the  same  time,  their  appearance  differs  more  or  less  from  that  observed 
when  they  are  seen  separately.  Thus  a  red  object  (e.g.  a  red  rose) 
appears  more  brilliant  if  a  green  object  be  seen  in  juxtaposition  with  it. 
Such  effects  are  said  to  be  due  to  contrast. 

When  any  two  colors  given  in  the  circle  (Plate  I.)  are  brought  in 
contrast,  as  when  they  are  placed  next  each  other,  the  effect  is  to  move 
them  farther  apart  in  the  color  scale.  For  example,  if  red  and  orange  be 
brought  in  contrast,  the  orange  assumes  more  of  a  yellowish  hue,  and  the 
red  more  of  a  purplish  hue.  Colors  that  are  already  as  far  apart  as 
possible,  e.g.  yellow  and  blue,  do  not  change  their  hue,  but  merely  cause 
each  other  to  appear  more  brilliant. 


342  RADIANT   ENERGY. 

327.  Color-blindness.  —  In  this  defect  in  vision,  one  of  the 
three  color  sensations  is  either  wanting  or  deficient,  usually  that  of  red  ; 
so  that  the  colors  perceived  are  reduced  to  those  furnished  by  the  remain- 
ing two  sensations,  viz.  green  and  violet.  This  causes  the  red-blind 
person  to  confound  reds,  greens,  and  grays.  In  some  rare  cases  the 
sensation  of  green  or  violet  is  the  one  deficient. 


Section  IX. 

THERMAL   EFFECTS    OF   RADIATION. 

328.  Heat  not  transmitted  by  Radiation.  —  We  have 
learned   that   heat   may  travel  through   matter    (by  con- 
duction), and  with   matter  (by  convection),  and  it  is  some- 
times stated  that  there  is  a  third  method  by  which  it 
travels,  viz.  "radiation."     Heat  itself  is  not  transferred 
by  radiation ;  heat  generates  radiation  (i.e.  ether  waves)  at 
one   place,    and   radiation    is   transformed    into    heat   at 
another.     Radiation   travels,    not   heat.     Heat   can    flow 
only  one  way,  viz.  from  a  given  point  to  a  point  that  is 
colder ;    radiation   travels   in   all    directions.      The   sun 
sends  us  no  heat;    it  sends  radiations  which  the  earth 
transforms  into  heat ;  but  it  should  be  borne  in  mind  that 
while  it  is  radiation  it  is  not  heat,  and  vice  versa.     Tem- 
perature   is    a   condition    of   bodies,    not    of    radiations  ; 
wave-lengths   belong   to   radiations,   not   to   heat  which 
produces  them. 

329.  Diathermancy    and    Athermancy.  —  What   be- 
comes of  radiations  which  strike  a  body  depends  largely 
upon  the  character  of  the   body.     If  the  nature  of  the 


THERMAL   EFFECTS   OF    RADIATION. 


343 


body  be  such  that  its  molecules  can  accept  the  motion  of 
the  ether,  the  vibrations  of  the  ether  are  said  to  be 
absorbed  by  the  body,  and  the  body  is  thereby  heated, 
i.e.  the  undulations  of  the  ether  are  transformed  into 
molecular  energy  or  heat.  Glass*  for  instance,  allows  the 
sun's  radiations  to  pass  very  freely  through  it,  and  very 
little  is  transformed  into  heat.  But  if  the  glass  be 
covered  with  the  soot  of  a  candle  flame,  the  soot  will 
absorb  the  radiations  and  the  glass  become  heated. 
Observe  how  cold  window-glass  may  remain,  while  radia- 
tions pour  through  it  and  heat  objects  in  the  room.  Only 
those  radiations  that  a  body  absorbs  heat  it;  those  that  pass 
through  it  do  not  affect  its  temperature. 

Bodies  that  transmit  radiations  freely  are  said  to  be 
diathermanous,  while  those  that  absorb  them  largely  are 
called  athermanous.  The  most  diathermanous  substance 
known  is  rock  salt.  A  solution  of  iodine  in  carbon 
bisulphide  absorbs  almost  completely  the  rays  of  the 
visible  spectrum,  but  transmits  almost  completely  all  of 
longer  wave-length  than  the  red  end  of  the  spectrum.  A 
plate  of  alum  acts  in  the  reverse  man- 
ner, transmitting  the  visible  and  absorb- 
ing the  invisible.  Among  liquids  carbon 
bisulphide  is  exceptionally  transparent 
to  all  forms  of  radiation;  while  water, 
transparent  to  short  waves,  absorbs  the 
longer  waves,  and  is  thus  quite  ather- 
manous. 


Experiment  234.  —  Prepare  a  differential 
thermometer  with  two  glass  flasks  and  a  glass 
tube,  as  represented  in  Figure  302.  Cover  one 


Fig.  303. 


344  RADIANT   ENERGY. 

of  the  flasks  with  lamp-black  by  holding  it  above  a  smoking  kerosene 
flame.  Place  colored  liquid  in  the  bend  A.  Stopper  both  vessels 
tightly  and  expose  the  apparatus  to  the  direct  rays  of  the  sun.  The 
rays  pass  through  the  clean  glass  and  through  the  air  within, 
affecting  the  temperature  of  either  but  little.  But  the  lamp-black 
absorbs  the  radiations,  the 'flask  becomes  heated,  the  enclosed  air 
becomes  heated  by  contact  with  the  heated  flask,  the  heated  air 
expands  and  pushes  the  liquid  in  the  tube  toward  the  cooler  flask. 

Dry  air  is  almost  perfectly  diathermanous.  All  of  the  sun's  radiations 
that  reach  the  earth  pass  through  the  atmosphere,  which  contains  a  vast 
amount  of  aqueous  vapor.  This  vapor,  like  water,  is  comparatively 
opaque  to  long  waves. 

This  fact  has  great  influence  in  modifying  the  climate  of  the  earth. 
For  the  earth,  warmed  by  the  sun's  radiations,  tends  also  to  part  with  its 
heat  by  radiation.  But  the  character  of  the  radiations  emitted  by  the 
earth  is  quite  different  from  that  of  the  radiations  which  it  receives. 
The  earth  at  a  low  temperature  emits  chiefly  long  ether  waves,  but  it  is 
heated  chiefly  by  short  waves.  But  it  is  exactly  these  long  waves  which 
are  most  readily  stopped  by  the  atmosphere  ;  hence,  the  atmosphere,  or 
rather  the  aqueous  vapor  of  the  atmosphere,  acts  as  a  sort  of  trap  for  the 
energy  which  comes  to  us  from  the  sun. 

Remove  the  watery  vapor  (which  serves  as  a  "  blanket "  to  the  earth) 
from  our  atmosphere,  and  the  chill  resulting  from  the  rapid  escape  of  heat 
by  radiation  would  probably  put  an  end  to  all  animal  and  vegetable  life. 

33O.  Provost's  Theory  of  Exchanges.  —  Hot  bodies  usually 
part  with  their  heat  much  more  rapidly  by  radiation  than  by  all  other 
processes  combined.  But  cold  bodies,  like  ice,  emit  radiations  even  when 
surrounded  by  warm  bodies.  This  must  be  so  from  the  nature  of  the  case, 
for  the  molecules  of  the  coldest  bodies  possess  some  motion,  and  being 
surrounded  by  the  ether  they  cannot  move  without  imparting  some  of 
their  motion  to  the  ether,  and  to  that  extent  becoming  themselves  colder. 

Let  us  suppose  that  we  have  two  bodies,  A  and  B,  at  different 
temperatures,  —  A  warmer  than  B.  Radiation  takes  place  not  only  from 
A  to  B,  but  from  B  to  A  ;  but,  in  consequence  of  A's  excess  of  tempera- 
ture, more  radiation  passes  from  A  to  B  than  from  B  to  A,  and  this 
continues  until  both  bodies  acquire  the  same  temperature.  At  this  point 
radiation  by  no  means  ceases,  but  each  now  gives  as  much  as  it  receives, 
and  thus  equilibrium  is  kept  up.  This  is  known  as  "Provost's  Theory 
of  Exchanges." 


THERMAL   EFFECTS    OF   RADIATION.  345 

331.  Good  Absorbers,  Good  Radiators.  —  As  bodies 
differ  widely  in  their  absorbing  power,  so  they  do  in  their 
radiating  power,  and  it  is  found  to  be  universally  true 
that  good  absorbers  are  good  radiators,  and  bad  absorbers 
are  bad  radiators.  Much,  in  both  cases,  depends  upon 
the  character  of  the  surface  as  well  as  of  the  substance. 
Bright,  polished  surfaces  are  poor  absorbers  and  poor 
radiators  ;  while  tarnished,  dark,  and  roughened  surfaces 
absorb  and  radiate  rapidly.  Dark  clothing  absorbs  and 
radiates  more  rapidly  than  light  clothing. 

QUESTIONS. 

1.  What  objections  can  you  raise  to  the  term  "  radiant  heat "? 

2.  Explain  why  the  temperature  of  a  hotbed  is  above  that  of  the 
surrounding  air. 

3.  How  could  you  separate  the  dark  radiation  of  an  electric  arc 
lamp  from  the  luminous  radiation  ? 

4.  How  can  you  demonstrate   the   existence   of   ether  waves  of 
greater  length  than  the  light-giving  waves  ? 

5.  Ice  appears  to   radiate    cold.     Explain   the   phenomenon   by 
Provost's  theory. 

6.  What  parts  of  the  spectrum  are  invisible  to  the  eye  ? 

7.  On  what  does  the  color  of  bodies  primarily  depend? 

8.  What  agency  does  a  body  perform  in  determining  its  own 
color  when  illuminated  with  white  light  ? 

9.  a.  Why  is  grass  green  ?     b.  Snow  white  ?     c.  Soot  black  ? 

10.  What  utility  is  there  in  keeping  certain  parts  of  a  steam- 
engine  very  bright  ? 

11.  When  red  and  green  sensations  coexist,  what  is  the  resulting 
sensation  ? 

12.  Describe  the  surface  which  a  hot-water  vessel  should  have  in 
order  to  retain  its  heat  well. 


346 


RADIANT   ENERGY. 


Section    X. 


SOME   OPTICAL   INSTRUMENTS. 

332.  Compound  Microscope.  —  When  it  is  desired  to 
magnify  an  object  more  than  can  be  done  conveniently 
and  with  distinctness  by  a  single  lens,  two  convex  lenses 
are  used,  —  one,  O  (Fig.  303),  called  the  objective,  to  form 
a  magnified  real  image  a'  bf  of  the  object  a  b  ;  and  the 
other  E,  called  the  eye-piece,  to  magnify  this  image  so 
that  the  image  a'  b'  appears  of  the  size  a"  b".  Instead  of 
looking  at  the  object  as  when  we  use  a  simple  lens,  we 
look  at  the  real  inverted  image  a'  b'  of  the  object. 

This  represents  the  simplest  possible  form  of  the  compound  microscope. 

In  practice,  however,  the  construction 
is  more  complicated. 

Figure  304  represents  a  perspective 
and  a  sectional  view  of  a  simple  form 
of  a  modern  compound  microscope. 
The  body  of  the  instrument  consists  of 
a  series  of  brass  tubes  movable  one 
within  another.  In  the  upper  end  H 
is  the  ocular  or  eye-piece.  It  consists 
of  two  plano-convex  lenses  o  and  ?i, 
the  former  called  the  eye  lens,  the  latter 
called  the  field  lens.  This  combination 
tends  to  diminish  both  the  spherical 
and  the  chromatic  aberration  as  well 
as  to  increase  the  size  and  flatness  of  the  field  of  view. 

All  microscopes,  however,  should  be  furnished  with  an  achromatic 
objective.  This  consists  of  two  to  four  achromatic  lenses  (the  achromatic 
triplet,  the  most  common  form,  is  represented  on  an  enlarged  scale  at  L 
in  Figure  304),  combined  so  as  to  act  as  a  single  lens  of  short  focus.  By 
the  use  of  several  lenses,  the  aberrations  can  be  better  corrected  than 
with  a  single  lens. 


Fig.  303. 


SOME    OPTICAL   INSTRUMENTS. 


347 


The  object  to  be  examined  is  placed  on  a  stage  S,  and  if  the  object 
be  transparent,  it  is  strongly  illuminated  by  focusing  light  upon  it  by 
means  of  a  concave  mirror  M.  If  the  object  be  opaque,  it  is  illuminated 
by  light  directed  upon  it  obliquely  from  above  by  the  converging  lens  N. 


Fig.  304. 


333.  Magnifying  Power.  —  The  magnifying  power  of 
a  compound  microscope  is  the  product  of  the  respective 
magnifying  powers  of  the  object-glass  and  the  eye-piece  ; 
that  is,  if  the  first  magnify  20  times  and  the  other  ten 
times,  the  total  magnifying  power  is  200.  The  magnify- 


348  RADIANT    ENERGY. 

ing  power  is  determined  experimentally  by  means  of  a 
micrometer  scale,  for  a  description  of  which  the  student  is 
referred  to  technical  works  on  microscopy. 

334.  Telescopes.  —  Telescopes  are  used  to  view  (scope) 
objects  afar  off  (tele).  They  are  classified  as  astronomical 
or  terrestrial,  according  as  they  are  designed  to  be  used  in 
viewing  heavenly  bodies  or  terrestrial  objects  ;  reflecting 
or  refracting,  according  as  the  objective  is  a  concave 
mirror  or  a  converging  lens.  The  terrestrial  telescope 
differs  from  the  astronomical  in  producing  images  in  their 
true  position  without  inversion.  This  is  effected  by  means 
of  an  extra  object  lens,  which  corrects  the  inversion  of  the 
main  object  lens.  The  matter  of  inversion  is  of  little  or 
no  consequence  in  viewing  heavenly  bodies. 

The  refracting  astronomical  telescope  consists  essentially,  like  the 


Fig.  305. 

compound  microscope,  of  two  lenses.  The  object-glass  (O,  Fig.  305)  forms 
a  real  diminished  image  (a,  6)  of  the  object  A,  B;  this  image,  seen 
through  the  eye-glass  E,  appears  magnified  and  of  the  size  c,  d.  The 
object-glass  is  of  large  diameter,  in  order  to  collect  as  much  light  as 
possible  from  a  distant  object  for  a  better  illumination  of  the  image. 

This  telescope  is  analogous  to  the  microscope,  but  the  two  instruments 
differ  in  this  respect :  in  the  microscope,  the  object  being  very  near  the 
object-glass,  the  image  is  formed  much  beyond  the  principal  focus,  and  is 
greatly  magnified,  so  that  both  the  object-glass  and  the  eye-piece 
magnify ;  while  in  the  telescope,  the  heavenly  body  being  at  a  great 
distance,  the  incident  rays  are  practically  parallel,  and  the  image  formed 
by  the  object-glass  is  much  smaller  than  the  object.  The  use  of  the 


SOME    OPTICAL   INSTRUMENTS. 


349 


object-glass  is  to  collect  as  large  a  number  as  possible  of  the  greatly 
scattered  rays,  so  as  to  increase  the  brilliancy  of  the  image.  The  only 
magnification  which  can  occur  is  produced  by  the  eye-piece,  which 
ought  therefore  to  be  of  high  power.  The  magnifying  power  of  this 
instrument  equals  approximately  the  focal  length  of  the  object-glass  divided 
by  the  focal  length  of  the  eye-piece. 

335.  The  Human  Eye.  —  Fig.  306  represents  a  hori- 
zontal section  of  this  wonderful  organ.  Covering  the 
front  of  the  eye,  like  a  watch- 
crystal,  is  a  transparent  coat 
1,  called  the  cornea.  A  tough 
membrane  2,  of  which  the 
cornea  is  a  continuation,  forms 
the  outer  wall  of  the  eye,  and 
is  called  the  sclerotic  coat,  or 
"  white  of  the  eye."  This  coat 
is  lined  on  the  interior  with  a 
delicate  membrane  3,  called 
the  choroid  coat;  the  latter 
consists  of  a  black  pigment,  which  prevents  internal 
reflection.  The  inmost  coat  4,  called  the  retina,  is  formed 
by  expansion  of  the  optic  nerve  O.  The  muscular  tissue 
i,  i  is  called  the  iris;  its  color  determines  the  so-called 
"  color  of  the  eye."  In  the  center  of  the  iris  is  a  circular 
opening  5,  called  the  pupil,  whose  function  is  to  regulate, 
by  involuntary  enlargement  and  contraction,  the  quantity 
of  light-waves  admitted  to  the  posterior  chamber  of  the  eye. 
Just  back  of  the  iris  is  a  tough,  elastic,  and  transparent 
body  6,  called  the  crystalline  lens.  This  lens  divides  the 
eye  into  two  chambers  ;  the  anterior  chamber  7,  is  filled 
with  a  limpid  liquid,  called  the  aqueous  humor;  the 
posterior  chamber  8,  is  filled  with  a  jelly-like  substance, 


350  RADIANT    ENERGY. 

called  the  vitreous  humor.  The  lens  and  the  two  humors 
constitute  the  refracting  apparatus. 

The  eye  may  be  likened  to  a  photographer's  camera,  in 
which  the  retina  takes  the  place  of  the  sensitized  plate. 
Images  of  outside  objects  are  projected  by  means  of  the 
crystalline  lens,  assisted  by  the  refraction  of  the  humors, 
upon  this  screen,  and  the  impressions  thereby  made  on 
this  delicate  network  of  nerve  filaments  are  conveyed  by 
the  optic  nerve  to  the  brain. 

With  the  ordinary  camera,  the  distance  of  the  lens  from 
the  screen  must  be  regulated  to  adapt  itself  to  the  varying 
distances  of  outside  objects,  in  order  that  the  images  may 
be  properly  focused  on  the  screen.  In  the  eye  this  is 
accomplished  by  changing  the  convexity  of  the  lens.  We 
can  almost  instantly  and  unconsciously  change  the  lens  of 
the  eye,  so  as  to  form  on  the  retina  a  distinct  image  of  an 
object  miles  away,  or  only  a  few  inches  distant.  The 
nearest  limit  at  which  an  object  can  be  placed  so  as  to 
form  a  distinct  image  on  the  retina  is  about  five  inches. 
On  the  other  hand,  the  normal  eye  in  a  passive  state  is 
adjusted  for  objects  at  an  infinite  distance. 

336.  Defects  of  Vision.  —  Myopia  (short-sightedness)  is  caused 
by  the  excessive  length  of  the  globe  from  front  to  back,  so  that  the 
images  of  all  but  near  objects  are  formed  in  front  of  the  retina. 
Remedy  :  use  diverging  lenses.  Hypermetropia  (long-sightedness)  occurs 
when  the  axis  of  the  globe  is  so  short  that  the  image  of  an  object  is  back 
of  the  retina  unless  the  object  is  held  at  an  inconvenient  distance,  in 
which  case  it  tends  to  become  indistinct.  Remedy  :  use  converging 
lens.  Presbyopia  is  due  to  loss  of  accommodation  power,  so  that  while 
vision  for  distant  objects  remains  clear,  that  for  near  objects  is  indistinct. 
This  defect  is  incident  to  advancing  years,  and  is  due  to  progressive  loss 
of  elasticity  of  the  crystalline  lens.  Remedy  :  converging  lenses.  Astig- 
matism is  caused  by  an  inequality  in  the  curvature  of  the  cornea  in 


SOME    OPTICAL    INSTRUMENTS. 


351 


different  meridians,  so  that  when,  for  example,  a  diagram  like  Figure  307 
is  held  at  a  distance,  vertical  lines  will  be  in  focus  and  horizontal  lines 
will  be  out  of  focus  and  will  appear  blurred 
and    indistinct,    or    vice    versa.     Remedy : 
lenses  of  cylindrical   curvature.     But,  for 
this,  as  well   as  for  all   other  defects  or 
troubles  of  the  eyes,  consult  a  skilled  ocu- 
list, and  the  earlier  the  better. 

Advice  to  all :  Do  not  overstrain  or  over- 
tax the  eyes,  or  use  them  in  insufficient  or 
excessive  light,  in  flickering  light  such  as 
that  of  a  gas-jet,  or  in  unsteady  light  such 
as  that  in  a  moving  vehicle  ;  and  avoid  so 
far  as  practicable  sudden  changes  of  light, 
such  as  lightning  flashes,  etc. 

337.  Stereopticon.  —  This  instrument  is  extensively 
employed  in  the  lecture-room  for  producing  on  a  screen 
magnified  images  of  small,  transparent  pictures  on  glass, 
called  slides ;  also  for  rendering  a  certain  class  of  experi- 
ments visible  to  a  large  audience  by  projecting  them  on  a 
screen.1  The  lime  light  is  most  commonly  used,  though 
the  electric  light  is  preferred  for  a  certain  class  of  pro- 
jections. The  flame  of  an  oxyhydrogen  blow-pipe,  A 
(Fig.  308),  is  directed  against  a  stick  of  lime  B,  and 


Fig.  307. 


Fig.  308. 


1  For  useful  information  relating  to  the  operation  of  projection,  especially  for 
scientific  illustrations,  see  Wright's  Light,  and  Dolbear's  Art  of  Projecting. 


352  RADIANT   ENERGY. 

raises  it  to  a  white  heat.  The  radiations  from  the  lime 
are  condensed  by  means  of  a  convex  lens  <?,  called  the  con- 
densing lens  (usually  two  plano-convex  lenses  are  used),  so 
that  a  larger  quantity  of  radiations  will  pass  through  the 
convex  lens  E,  called  the  projecting  lens.  The  latter  lens 
produces  (or  projects)  a  real,  inverted,  and  magnified 
image  of  the  picture  on  the  screen  S.  The  mounted  lens 
E  may  slide  back  and  forth  on  the  bar  F,  so  as  properly  to 
focus  the  image. 

EXERCISES. 

1.  What  is  light? 

2.  State  points  of  resemblance  and  points  of  difference  between 
light-waves  and  sound-waves.     Which  can  traverse  a  vacuum   (as 
regards  matter)? 

3.  Two  books  are  held,  respectively,  2  feet  and  7  feet  from  the 
same  gas-flame.     Compare  the  intensities  of  the  illumination  of  their 
respective  pages. 

4.  What  is  the  general  effect  of  a  concave  mirror  on  light-waves  ? 
What  kind  of  lens  produces  a  similar  effect  ? 

5.  How  can  a  beam  of  light  be  bent  ? 

6.  State  different  ways  by  which  the  colors  which  compose  white 
light  may  be  revealed. 

7.  How  do  you  account  for  the  color  of  flowers?     How  do  you 
account  for  the  colors  seen  on  a  soap-bubble  ? 

8.  Why  do  white  surfaces  appear  gray  at  twilight  ? 

9.  How  are  objects  heated  by  the  sun  ? 

10.  What  evidences  can  you  give  that  the  earth  receives  energy 
from  the  sun  ? 

11.  What  phenomenon  shows  that  ether-waves  do  not  traverse  all 
substances  with  equal  speed  ? 


REVIEW   QUESTIONS.  853 


REVIEW    QUESTIONS. 

1.  Show    that   a  spring  balance    is,   strictly   speaking,    a   force- 
measurer,  and  not  a  mass-measurer. 

2.  A  body  weighs  100  Ibs.  at  the  earth's  surface.     Where  would 
it  weigh  on  a  spring  balance  50  Ibs.  ? 

3.  What   way   of   measuring   force    is   suggested    by    Newton's 
Second  Law  of  Motion  ? 

4.  Determine  the  available  water  pressure  (in  pounds  per  square 
inch)  in  a  laboratory  which  is  supplied  from  a  tank  at  a  hight  of 
45ft. 

5.  What  is  the  atmospheric  pressure  in  pounds  per  square  inch 
when  the  barometric  height  is  27.5  in.? 

6.  What   should  be  the   horse-power  of   an  engine  intended  to 
pump   200    gallons    of   water   per    minute    to  a   hight  of   50   yds.  ? 
(Assume  1  gall.  =c=  10  Ibs.) 

7.  A  cube,  the  edge  of  which  is  one  decimeter,  is  suspended  in 
water  with  its  upper  surface  lm  below  the  surface  of   the  water. 
Find  the  pressure  on  each  of  its  faces. 

8.  A  sailor  climbs  a  mast  at  a  uniform  rate  of  5  ft.  a  minute, 
while  the  vessel  moves  forward  at  the  rate  of  15  ft.  a  minute  ;  what 
is  his  actual  velocity  ? 

9.  If  the  masses  of  a  rifle  and  a  bullet  be  respectively  25  Ibs.  arid 
1  oz.  (y^  lb.),  and  the  rifle  at  its  discharge  acquire  a  maximum 
velocity  of  3  ft.  per  second,  what,  at  that  instant,  is  the  velocity  of 
the  bullet  ? 

10.  If  the  motion  of  the  moon  in  its  orbit  about  the  earth  were 
to  cease,  these  bodies  would  approach  each  other.     The  mass  of  the 
earth  is  about  80  times  that  of  the  moon.     What  part  of  the  whole 
distance  between  them  would  the  moon  move  before  collision  ? 

11.  A  constant  force  acts  on  an  otherwises  freely  moving  body  in  a 
direction  opposite  to  that  in  which  it  is  moving  ;  how  is  the  body's 
motion  affected  thereby  ?     Give  an  illustration. 

12.  State  and  explain  the  posture  of  a  bicycle-rider  in  turning 
a  curve. 


354  RADIANT    ENERGY. 

13.  Account  for  the  curvilinear  orbits  of  the  planets. 

14.  A  pebble  is  suspended  by  a  thread  2  ft.  long  ;  required  the 
number  of  vibrations  it  will  make  in  a  minute. 

15.  Suppose  that  in  bending  a  bow  an  average  force  of  25  Ibs.  is 
exerted  through  a  space  of  10  inches  ;  what  amount  of  energy  will 
be  stored  in  the  bow  ? 

16.  A  projectile  of  a  mass  of  50 k  is  thrown  vertically  upward 
with  an  initial  velocity  of  29.4ra  per  second.     How  much  energy 
has  it  ? 

17.  How  many  and  what  transformations  of  energy  take  place 
during  a  single  swing  of  a  pendulum  ? 

18.  Supply  the  following  ellipses  by  selecting  appropriate  words 
from  the  following,  viz.:    Force,  work,  energy,  power.     When  — 

acts  through  space is  performed,  and is  imparted.      The 

rate  at  which  work  is  performed  determines  the of  the  agent. 

The of  a  bullet  flying  through  vacant  space.     What  —    —  must 

a  bullet  of  mass  1  ounce  have  that  it  may  rise  4  seconds  ?     What 

—  is  consumed  by  a  steamer  in  crossing  the  ocean  ?    What  —  —  is 
necessary  that  it  may  traverse  300  knots  per  day,  and  what  must  be 

the  average exerted  to  overcome  the  resistances  at  the  required 

rate? 

1 9.  Change  of  momentum  is  proportional  to  what  ?     Change  of 
energy  is  proportional  to  what  ? 

20.  A  building  is   heated  by  steam-pipes.     How  does  heat  get 
from  the  furnace  to  objects  in  the  building? 

21.  A  mass  of  93.3s  of  copper  at  80°  C.  is  immersed  in  560 §  of 
water  at  10°,  and  raises  the  temperature  of  the  water  to  20°;  find 
the  specific  heat  of  copper. 

22.  How  much  ice  at  0°  will  be  melted  by  400 «  of  water  at  90°  C  ? 

23.  Copper  wire  ^  in.  in  diameter  offers  a  resistance  of  8  ohms 
per  mile  ;  what  is  the  resistance  of  a  mile  of  copper  wire  -fa  in.  in 
diameter  ? 

24.  a.  How  many  volts  are  required  to   maintain   a   5-ampere 
current  in  a  circuit  whose  resistance  is  2  ohms  ?     b.  What  power  is 
consumed  in  the  circuit  ? 

25.  Determine  the  amperage   of  a  battery  of  5  cells  joined  in 
multiple  arc,  each  having  an  E.M.F.   of  2  volts  and  an  internal 


REVIEW    QUESTIONS.  355 

resistance  of  .5  ohm,   (a)  when  the  external  resistance  is  .1   ohm  ; 
(6)  when  the  external  resistance  is  500  ohms. 

26.  What  are  induced  currents  ?     how  produced  ?     how    made 
continuous-  ? 

27.  Upon  what  does  the  E.M.F.  of  a  dynamo  depend? 

28.  A  dynamo  feeds  16  arc  lamps  that  have  an  average  resistance 
of  4.56  ohms.     What  current  does  the  dynamo  yield  with  an  E.M.F. 
of  838.44  volts  ? 

29.  What  is  the  length  of  sound-waves  yielded  by  a  c'  fork  when 
the  temperature  of  the  air  is  18°  C.  ? 

30.  A  string  sounding  the  tone  c'  is  18  in.  long.     What  must  be 
its  length  to  sound  cf  ? 

31.  If  you  hold  a  sheet  of  paper  with  a  greased  spot  on  it  between 
you  and  a  gas-flame  in  a  darkened  room,  will  the  spot  appear  lighter 
or  darker  than  the  rest  of  the  sheet  ?     Why  ? 

32.  The  focal  length  of  a  convex  lens  being  8  in.,  determine  the 
position  of  the  conjugate  focus  of  a  point  15  in.  from  the  lens. 

33.  Why  is  pulverized  glass  opaque? 

34.  Under  what  conditions  will  a  spectrum  be  continuous  ?  bright- 
line  ?   dark-line  ? 

35.  A  person  whose  distance  of  most  distinct  vision  is  20 cm  uses 
a  lens  of  5 cm  focal  length  as  a  reading-glass,     a.  At  what  distance 
from  a  book  ought  he  to  hold  it  ?     b.  What  will  be  its  magnifying 
power  ? 


Inches 


i 

2                                        |3 

lUlll]  llll               \2 

|3               14 

Ic 

7               Is               9 

1C 

Millimeters 


Centimeters 


Mil  lil'lte 


Cubic  Centimeter 

The  area  of  this  figure  is  a  square  decimeter. 
A  cube  of  water,  one  of  whose  sides  has  this 
area,  is  a  cubic  decimeter  or  a  liter  of  water, 
and  at  the  temperature  of  4°  C.  has  a  mass  of 
a  kilogram.  The  same  volume  of  air  at  0°  C., 
and  under  a  pressure  of  one  atmosphere,  has  a 
mass  of  1.293  grams.  The  gram  is  the  mass 
of  1  cc  of  pure  water  at  4°  C. 


Square    j 
Centimeter- 


Square  Inch 


12              345              67              8              9            10 

10  Centimeters 

1 

\          \ 

1 

I 

I 

\          \ 

1 

1 

iHQJ]  S2  IM 

iMMIl 

!!  ill  III  I!  PI 

!  i  i 

MM 

mL  ttHL 

1.1,  iii." 

:NN|'L 

100  Millimeters 


-^,JFO 

DEPARTMENT  OF  PHYSICS 


APPENDIX. 


SECTION   A. 

Metric  system  of  measures.  —  The  term  metric  is  derived  from 
the  word  meter,  which  is  the  name  of  the  fundamental  unit  employed 
in  this  system  for  measuring  length,  and  from  which  all  other  units 
of  the  system  are  derived.  The  meter  is,  approximately,  the  ten- 
millionth  part  of  the  distance  from  the  Equator  to  the  North  Pole. 
Defined  by  law,  it  is  the  distance  at  0°  C.  between  two  lines  engraved 
on  a  platinum  bar  kept  in  the  Paris  Observatory.  The  gram  is  theo- 
retically the  mass  of  Ice  of  distilled  water  at  4°  C.  By  law  it  is  y^ 
of  the  mass  of  a  piece  of  platinum  preserved  in  the  same  observatory. 
At  Washington  are  kept  exact  copies  of  the  meter  and  other  metric 
measures. 

The  following  tables  contain  all  the  requirements  of  this  book.  The 
pupil  will  find  more  complete  tables  in  any  good  arithmetic. 

TABLE  OF  LENGTHS. 

10  millimeters  (mm)  =  1  centimeter  (cm). 
10  centimeters  =  1  decimeter  (dm). 
10  decimeters  =  1  meter  (m). 

1000  meters  =  1  kilometer  (km). 

TABLE  OF  AREAS. 

100  square  millimeters  (qn»m)  =  1  square  centimeter  (Q"0). 
100  square  centimeters  =  1  square  decimeter  (qdm). 

100  square  decimeters  =  1  square  meter  (q»n). 

1,000,000  square  meters  —  1  square  kilometer  (Q*m). 


358  APPENDIX. 


TABLE  OF  VOLUMES. 

1000  cubic  millimeters  (cm™)  =  1  cubic  centimeter  (ccmorcc). 
1000  cubic  centimeters  =  1  cubic  decimeter  (cdm). 

1000  cubic  decimeters  =  1  cubic  meter  (cbm). 

The  volumes  of  liquids  and  gases  are  either  expressed  in  the  units 
of  the  above  table  or  in  liters.     The  liter  is  lcdm,  or  1000CC. 


TABLE  OF  MASSES  OR  WEIGHTS. 

10  milligrams  (ms)  =  1  centigram  (cg). 
10  centigrams  =  1  decigram  (d£). 
10  decigrams  =  1  gram  (s). 

1000  grams  =  1  kilogram  or  kilo  (k). 


TABLE  OF  EQUIVALENTS. 

1  inch  =       0.0254  meter,    or  about  2|  centimeters. 
1  foot  =       0.3048  meter,    or  about  30  centimeters. 
1  yard  —       0.9144  meter,    or  about  |£  meter. 
1  mile  =  1609.0000  meters,  or  about  1T%  kilometers. 


i  TT  «  J  liquid  rtlll,t      i  0.94G  liter, 
1U.S.-J  d^y      quart  H  ^oi  liters, 

1  U.S.  gallon  =  3.785  liters,  or  about  3r%  liters. 

,  i  avoirdupois  i   0.02835  kilo,  «,       i  less 

H  Troy  and  apothecaries'   ounce  =  ^   0.03110  kilo,  orrather1  more 
than  30  grams. 

1  avoirdupois  pound  =  0.45359  kilo,  or  about  ^  kilo. 

When  great  accuracy  is  not  required,  it  will  be  found  convenient  to, 
remember  that 

centimeters  X  f  =  inches  (nearly)  ; 
inches  X  f  —  centimeters  (nearly)  ; 

5  meters  =  1  rod  (nearly)  ; 

also,  kilos  X  ^  —  pounds  (nearly)  ; 

pounds         X  fV  =  kilos  (nearly). 


APPENDIX. 


359 


SECTION   B. 

TABLES    OF    SPECIFIC    GRAVITIES    OF   BODIES. 
[The  standard  employed  in  the  tables  of  solids  and  liquids  is  distilled  water  at  4°  C.] 

I.  Solids. 


Antimony 6.712 

Bismuth 9.822 

Brass 8.380 

Copper,  cast 8.790 

Iridium 23.000 

Iron,  cast 7.210 

Iron,  bar 7.780 

Gold 19.360 

Lead,  cast 11.350 

Platinum 22.069 

Silver,  cast 10.470 

Tiu,cast 7.290 

Zinc,  cast 6.860 

Anthracite  coal 1.800 

Bituminous  coal. .  1.250 


Diamond 3.530 

Glass,  flint 3.400 

Human  body 0.890 

Ice 0.920 

Quartz 2.650 

Rock  salt 2.257 

Saltpetre 1.900 

Sulphur,  native 2.033 

Tallow 0.942 

Wax 0.969 

Cork 0.240 

Pine 0.650 

Oak 0.845 

Beech 0.852 

Ebony 1.187 


II.    Liquids. 


Alcohol,  absolute 0.800 

Bisulphide  of  carbon 1.293 

Ether 0.723 

Hydrochloric  acid 1.240 

Mercury 13.598 

Milk • 1.032 

Naphtha 0.847 


Nitric  acid 1.420 

Oil  of  turpentine 0.870 

Olive  oil 0.915 

Sea  water 1 .026 

Sulphuric  acid 1.841 

Water,  4°  C. ,  distilled ...  1 .000 

Water,  0°  C. ,  distilled . .  0.999 


III.    Gases. 
•  [Standard  :  air  at  0°  C. ;  barometer, 


Air 1.0000 

Ammonia 0.5367 

Carbonic  acid 1.5290 

Chlorine 3.4400 

Hydrochloric  acid 1.2540 


Hydrogen 0.0693 

Nitrogen 0.9714 

Oxygen 1.1057 

Sulphuretted  hydrogen..  1.1912 
Sulphurous  acid 2.2474 


360 


APPENDIX. 


SECTION   C. 

TABLE  OF  NATURAL  TANGENTS. 


Deg. 

Tangent. 

Deg. 

Tangent. 

Deg. 

Tangent. 

Deg. 

Tangent. 

1 

.017 

24 

.445 

47 

1.07 

70 

2.75 

2 

.035 

25 

.466 

48 

1.11 

71 

2.90 

3 

.052 

26 

.488 

49 

1.15 

72 

3.08 

4 

.070 

27 

.510 

50 

1.19 

73 

3.27 

5 

.087 

28 

.532 

51 

1.23 

74 

3.49 

C 

.105 

29 

.554 

52 

1.28 

75 

3.73 

7 

.123 

30 

.577 

53 

1.33 

76 

4.01 

8 

.141 

.31 

.601 

54 

1.38 

77 

4.33 

9 

.158 

32 

.625 

55 

1.43 

78 

4.70 

10 

.176 

33 

.649 

56 

1.48 

79 

5.14 

11 

.194 

34 

.675 

57 

1.54 

80 

5.67 

12 

.213 

35 

.700 

58 

1.60 

81 

6.31 

13 

.231 

36 

.727 

59 

1.66 

82 

7.12 

14 

.249 

37 

.754 

60 

1.73 

83 

8.14 

15 

.268 

38 

.781 

61 

1.80 

84 

9.51 

16 

.287 

39 

.810 

62 

1.88 

85 

11.43 

17 

.306 

40 

.839 

63 

1.96 

86 

14.30 

18 

.325 

41 

.869 

64 

2.05 

87 

19.08 

19 

.344 

42 

.900 

65 

2.14 

88 

28.64 

20 

.364 

43 

.933 

66 

2.25 

89 

57.29 

21 

.384 

44 

.966 

67 

2.36 

90 

Infinite. 

22 

.404 

45 

1.000 

68 

2.48 

23 

.424 

46 

1.036 

69 

2.61 

APPENDIX.  361 

SECTION  D. 

SIMPLE    PENDULUM.       CENTER    OF    OSCILLATION. 

A  simple  pendulum  is  a  material  particle  supported  by  a  weightless 
thread.  Such  a  pendulum  can  sxist  only  in  the  imagination,  but  the 
conception  is  useful.  Every  real  pendulum  is  a  compound  pendulum, 
which  may  be  supposed  to  be  composed  of  as  many  simple  pendulums 
bound  together  as  there  are  particles  in  the  pendulum.  Those  particles 
nearest  the  point  of  suspension  tend  to  quicken,  and  those  farthest  away 
tend  to  check,  the  motion  of  the  combination.  It  is  apparent  that  there 
must  be  in  every  compound  pendulum  a  particle  so  situated  that  its 
motion  is  neither  quickened  nor  checked  by  the  combined  action  of  the 
particles  above  and  below  it.  The  location  of  this  particle  is  called 
the  center  of  oscillation.  The  real  length  of  a  compound  pendulum  is  the 
distance  of  this  point  from  the  point  of  suspension,  and  it  is  this  length 
that  is  referred  to  in  the  laws  of  the  pendulum,  page  96. 

The  center  of  oscillation  of  a  pendulum  may  be  found  approximately 
as  follows  :  A  small  lead  ball  suspended  by  a  thread  is  a  near  approxima- 
tion to  a  simple  pendulum,  and  the  distance  from  the  center  of  the  ball  to 
the  point  of  suspension  may  be  taken  as  the  length  of  this  pendulum. 
Suspend  from  the  same  support  this  pendulum  and  the  pendulum  whose 
center  of  oscillation  is  to  be  found.  For  example,  let  the  pendulum 
be  a  lath  (Fig.  309)  suspended  at  its  upper  extremity  A. 
Lengthen  or  shorten  the  ball  pendulum  till  it  swings  in  the 
same  time  as  the  lath.  Then  the  true  lengths,  of  the  two 
pendulums  must  be  the  same.  Lay  off  on  the  lath  from  its 
point  of  suspension  a  distance  equal  to  the  distance  from 
the  point  of  suspension  to  the  center  of  the  ball,  and  this 
will  give  the  center  of  oscillation  of  the  lath  pendulum. 
This  point,  in  case  the  lath  be  of  uniform  dimensions  and 
density  throughout,  will  be  at  C,  about  two-thirds  the  length 
of  the  lath  from  its  point  of  suspension  A. 

If  a  weight  (or  "  bob  ")  be  attached  to  the  lower  end  of 
A  B,  its  center  of  oscillation  is  moved  lower  and  the  period    Fig  3O9 
of  vibration  is  lengthened.     If  the  bob  of  a  pendulum  be 
raised  (usually  by  turning  a  thumb-screw  just  beneath  it)  the  pendulum 
is  shortened  and  its  rate  of  vibration  is  increased. 


362  APPENDIX. 

The  isochronism  of  the  pendulum  is  utilized  in  the  measurement  of 
time,  i.e.  in  subdividing  the  solar  day  into  hours,  minutes,  and  seconds. 
The  office  of  the  pendulum  in  clocks  is  to  regulate  the  rate  of  motion  of 
the  works.  The  balance-wheel  replaces  the  pendulum  in  watches  and 
some  clocks. 

The  three  laws  of  the  pendulum  (pp.  95  and  96)  are  comprised  in  the 
formula 


t=  tf-y->  whence  g—  —  > 

in  which  Z  =  length  of  pendulum  ;  t  =  time  of  one  vibration  in  seconds. 
The  development  of  this  formula  may  be  found  in  Chapter  VII.  of 
Maxwell's  "Matter  and  Motion." 


APPENDIX.  363 

SECTION  B. 

EXPANSION-COEFFICIENTS. 

The  expansion  which  attends  a  rise  of  temperature  depends  not  only 
upon  the  size  of  the  body,  and  upon  the  number  of  temperature  degrees 
through  which  it  is  heated,  but  upon  a  quantity  peculiar  to  the  substance 
itself  called  its  expansion-coefficient.  This  term  is  applied  to  the  increase 
of  unit-length  per  degree  rise  of  temperature. 

Suppose  that  a  rod  of  length  I  at  0°  C.  be  heated  through  t  degrees,  so 
that  its  length  becomes  li  ;  then,  representing  the  linear  expansion- 
coefficient  by  c,  we  have 

c  —   1        ,  whence  li  =  l(l  +  ct). 

IT; 

The  expression  1  +  ct,  called  the  expansion-factor,  is  evidently  the 
ratio  of  the  final  to  the  original  length.  Hence  l\  —  I  (1  +  ct)  ;  that  is, 
multiplying  the  length  of  a  solid  at  0°  C.  by  the  expansion  factor  gives 
its  length  at  t  degrees  above  zero.  Conversely,  dividing  its  length  at  t° 
by  the  expansion  factor  gives  its  length  at  0°. 

TABLE  OF  MEAN  COEFFICIENTS  ON  LINEAR  EXPANSION  BETWEEN  0°  AND  100°  C. 


Platinum 

00000085 

Brass         . 

0000019 

Steel 
Wrought  iron 

0.000012 
0.000012 
0000011 

Silver 
Tin     . 
Lead 

0.000019 
0.000022 
0  000029 

Gold. 

0.000015 

Zinc  . 

0.000029 

In  the  expansion  of  fluids  we  have  to  do  only  with  increase  of  volume, 
called  volume  or  cubical  expansion.  A  volume-expansion-coefficient  is  the 
increase  of  unit-volume  per  degree  rise  of  temperature.  This  is  approxi- 
mately 3  c,  or  three  times  the  linear  expansion-coefficient,  and  may  be 
taken  as  such  for  most  practical  purposes.  Likewise,  the  surface  or 
superficial  expansion-coefficient  is  approximately  2  c. 

Not  only  do  the  expansion-coefficients  of  liquids  and  solids  vary  with 
the  substance,  but  the  coefficient  for  the  same  substance  varies  with  the 
temperature,  being  greater  at  high  than  at  low  temperatures.  Hence,  in 
giving  the  expansion-coefficient  of  any  substance  it  is  customary  to  give 
the  mean  coefficient  through  some  definite  range  of  temperature,  as  from 
0°  to  100°  C. 


364  APPENDIX. 


SECTION  F. 

TABLE    OF    ELECTRICAL    RESISTANCE    OF    WIRE. 

Chemically  pure,  one  meter  long,  one  millimeter  in  diameter, 

at  0°  C.  (Jenkin). 

Relative 
Resistances. 

Silver,  annealed 01937  ohm  1.000 

"      hard  drawn 02103  "  1.080 

Copper,          "               .         .         .         .         .02104  "  1.086 

Zinc,  pressed 07244  "  3.741 

Platinum 11660  "  0.022 

Iron,  annealed ,12510  "  6.400 

Lead,  pressed 25270  "  13.050 

German-silver                                          ,         .26950  "  13.920 


APPENDIX. 


365 


SECTION  G. 

DYNAMOS CONTINUED. 

All  figures  given  in  preceding  pages  have  been  diagrammatic  repre- 
sentations of  dynamos.  Figure  310  represents  a  modern  typical  dynamo, 
the  Weston.  Large  field  magnets,  A  and  B,  are  placed  each  side  of  the 
revolving  armature.  A  steam-engine  communicates  motion  to  the 


.  310. 


armature  by  means  of  a  belt  passing  over  the  circumference  of  the  wheel 
W.     The  magnets  are  shunt-  wound. 

Figure  311  represents  one  of  the  most  common  forms  of  the  Edison 
dynamo,  and  Figure  312  is  a  skeleton  diagram  corresponding  in  most 
particulars  with  the  first.  It  will  be  seen  by  the  latter  figure  that  it  is  a 
shunt-wound  dynamo.  The  terminals  of  an  automatic  regulator  for 
regulating  the  intensity  of  the  current  are  inserted  in  the  binding  screws 
a  a.  P  is  a  so-called  pilot-lamp  joined  in  multiple  arc  to  the  field-coils. 
F  F  are  leading  wires  ;  and  b  b  are  points  for  the  attachment  of  fuses. 


366 


APPENDIX. 


These  fuses  are  to  the  dynamo  what  the  safety-valve  is  to  the  steam 
boiler ;  they  protect  the  dynamo  from  injury  by  overpressure,  since  an 
overload  is  sure  to  cause  them  to  melt  and  thus  interrupt  the  current. 


Fig.  311. 

Classes  of  Armatures.1  —  (1)  In  ring-armatures  the  coils  are 
wound  round  a  ring-shaped  core.  Example  :  the  Gramme  and  the 
Brush. 

(2)  In  drum-armatures  the  coils  are   wound  longitudinally  over  a 
cylinder  or  drum,  as  in  Figure  313.    Examples :  the  Edison,  the  Weston, 
and  the  Siemens. 

(3)  In  pole  or  radial  armatures  the  coils  are  wound  on  separate  poles 
that  project  radially  from  a  cylinder  (Fig.  314). 

1  The  Thomson-Houston  armature  cannot  be  classified,  as  it  is  unique  among 
armatures.  It  is  spheroidal  in  shape. 


APPENDIX. 


367 


In  alternating-current  dynamos,  in  order  to  obtain  the  rapid  reversals 
(in  some  machines  as  many  as  200  per  second)  of  currents  in  opposition 
to  resistance  offered  by  self-induction,  a  number  of  poles  of  alternate 
polarity  are  employed. 


Fig.  313. 


Fig.  313. 


The  separate  coils  may  be  coupled  either  in  series  or  in  multiple  arc. 
When  low  E.M.F.  is  desired,  as  for  incandescent  lamps  in  multiple  arc, 
the  separate  coils  are  united  in  multiple  arc  ;  but  where  great  F/.M.F.  is 
required,  they  are  connected  in  series,  as  shown  in  Figures  314  and  315. 


Fig.  315. 

(4)  Disk-armatures  are  usually  composed  of  a  number  of  separate  coils 
set  side  by  side  in  the  circumference  of  a  disk  (Fig.  315).  Mechanical 
difficulties  in  their  construction  have  not  permitted  them  as  yet  to 
compete  successfully  with  the  first  two  types  named  above. 


368 


APPENDIX. 


SECTION  H. 


ELECTRIC    MOTORS CONTINUED. 


316. 


The  Action  of  the  Dynamo-Motor.  —  This  may  be  under- 
stood by  referring  to  Figure  316,  and  imagining  a  generator  to  replace 
the  external  resistance  R.  Suppose  the  current  from  the  generator  enters 
at  the  brushes  and  flows  in  the  loop  in  the  direction  of  the  arrows;  then 
the  upper  face  of  the  loop  will  have  S  polarity  and  the  under  face  N 
g  polarity.  Then  by  the  mutual 

action  between  this  field  and 
that  of  the  magnet  N  S,  a  rota- 
tion of  the  loop  will  take  place 
clockwise  till  it  comes  into 
a  vertical  position.  When  it 
reaches  this  position,  however, 
the  brushes  are  so  arranged 
with  reference  to  the  commu- 
tator segments  that  the  current 
in  the  loop  —  and  hence  its  polarity  —  is  reversed.  Even  if  there  were 
only  one  loop  its  inertia  would  be  sufficient  to  carry  it  by  this  critical 
position,  and  the  loop  would  continue  to  rotate  in  the  attempt  again  to 
bring  its  field  parallel  to  that  of  N  S  ;  but  as  a  matter  of  fact  the  other 
loops  in  the  armature  are  never  in  the  critical  position  at  the  same  time 
as  the  one  considered,  and  those  on  each  side  of  it  conspire  to  produce  a 
continuous  rotation  in  the  same  direction. 

If  the  armature  contain  a  soft  iron  core,  as  is  usually  the  case,  the 
intensity  of  the  field  will 
be  much  greater  and  the 
mechanical    effect    corre- 
spondingly increased. 

Figure  317  represents  a 
modern  form  of  motor 
weighing  only  two  or  three 
pounds,  and  capable,  when 
worked  with  four  or  five 
Bunsen  cells,  of  operating 
a  sewing-machine  or  run- 


Fig.  317. 


APPENDIX. 


369 


Fig.  318. 


ning  a  small  saw.     It  consists  of  a  movable  coil  within  a  fixed  coil.     The 
wires  of  each  coil  are  wound  on  an  iron  frame-work,  the  two  opposite 
edges  of  the  iron  being  north 
and  south  poles  when  the 
current  is  passing. 

The  inner  coil  is  fur- 
nished with  a  commutator, 
which  reverses  the  current 
as  soon  as  opposite  poles  of 
the  inner  and  outer  coils  are 
opposed.  A  represents  the 

outer  coil  of  wires,  B  one  pole  of  the  fixed  electro-magnet  made  by  it,  and 
C  the  commutator  by  which  the  inner  coil  has  the  current  reversed  each 

half  revolution.  Figure  318  shows 
the  inner  coil  D,  whose  terminals  are 
attached  to  the  two  halves  of  the  spin- 
dle E,  which  are  carefully  insulated 
from  each  other.  In  Figure  319  the 
commutator  is  shown  in  plan.  The 
current  enters  the  inner  coil  through 
the  spring  H,  which  carries  a  friction 
roller  working  on  the  commutator  E ; 
after  traversing  the  coil  it  returns  to 
the  upper  half  of  E,  and  thence  passes  by  the  spring  G  to  K,  from  K 
through  the  outer  coil  to  L,  and  from  L  back  to  the  battery. 

The  dynamo  as  a  generator  and  the  dynamo  as  a  motor  have  already 
revolutionized  electrical  economics  and  relegated  the  battery  to  an 
honored  position  among  things  of  the  past.  The  electric  motor  is  now 
extensively  used  in  large  towns  and  cities,  in  factories  where  power  is 
not  continuously  needed.  Its  widest  application  at  present  is  in  the 
propulsion  of  street  cars.  The  current  is  generated  by  dynamos  at  some 
central  power  house  and  thence  distributed  to  the  motors  at  various 
points  on  the  circuit. 


Fig.  319. 


INDEX. 


[Numbers  refer  to  pages.] 


Aberration,  Chromatic,  335;  Spheri- 
cal, 325. 

Absolute  temperature,  136;  zero, 
135. 

Accelerated  motion,  Laws  of,  89. 

Adhesion,  25. 

Air-pump,  41,  Mercury,  42. 

Amalgamating  zincs,  172. 

Ammeter,  187. 

Ampere,  182. 

Ampere's  theory  of  magnetism,  215; 
laws  of  currents,  215. 

Annealing,  23. 

Artificial  cold,  145. 


Barometer,  34 ;  Aneroid,  35. 
Batteries,  Electric,  196-198;   Stor- 
age, 234. 
Beats,  271. 
Boyle's  law,  40. 
Buoyant  force  of  fluids,  56. 


Capillary  phenomena,  27-28. 
Center  of  gravity,  82. 
Centrifugal  tendency,  93. 
Circuit,  Divided,  195;  Electric,  171. 


Cohesion,  19. 

Color  by  absorption,  336;  Cause  of, 
329. 

Color  vision,  Theory  of,  340. 

Colors,  Complementary,  340;  Mix- 
ing, 338;  Prismatic,  327. 

Commutator,  227. 

Compressibility  of  gases,  38. 

Condenser,  Air,  44. 

Contrast,  Effect  of,  341. 

Coulomb,  182. 

Couple,  Mechanical,  78. 

Critical  angle,  314. 

Crystallization,  20. 

Curvilinear  motion,  92. 


Density,  9,  59;  Specific,  60. 
Diathermancy,  139. 
Dielectric,  161. 
Distillation,  139. 
Ductility,  25. 

Dynamo,  223-230,  365-367. 
Dynamometers,  13. 

E 

Ear,  289. 

Elasticity,  24;  of  gases,  38. 
Electric  current,    170;    Effects   of, 
175-181 ;  Strength  of,  182. 


372 


INDEX. 


Electric  light,  236-239. 

Electric  motor,  230,  231,  368,  369. 

Electrical  induction,  161. 

Electricity,  Conduction  of,  160; 
What  is  it  ?  159. 

Electrification,  157,  158. 

Electrodes,  170,  176. 

Electrokinetics,  165,  169. 

Electrolysis,  175;  Reversibility  of, 
234. 

Electrolyte,  169. 

Electro-motive  force,  182;  of  dif- 
ferent cells,  194. 

Electroplating,  241. 

Electroscope,  159. 

Electrostatics,  165. 

Electrotyping,  239. 

Energy,  5,  100,  102,  103;  Conserv- 
ation and  correlation  of,  150 ; 
Kinetic  and  potential,  100;  Ra- 
diant, 292;  Unit  of,  101. 

Equilibrium,,  13,  77,  84. 

Ether,  The,  292. 

Evaporation,  140. 

Exchanges,  Prevost's  theory  of, 
344. 

Expansion,  130-132 ;  Abnormal, 
132. 

Extra  currents,  220. 

Eye,  349. 


Falling  bodies,  Laws  of,  87. 

Flexibility,  24. 

Fluids,  9;  Buoyant  force  of,  56; 
Elasticity  of,  38;  Measurement 
of  atmospheric,  33;  Pressure  in, 
29,  51. 

Foci,  Conjugate,  321. 

Force,  14 ;  Centripetal,  92 ;  Graph- 
ical representation  of,  71;  Gravi- 


tation units  of,  17;  How  meas- 
ured, 12. 

Forces,  Composition  of,  72,  75; 
Equilibrium  of,  13;  Molecular, 
18 ;  Resolution  of,  73. 

Focus,  Principal,  319. 


Galvanometer,  186. 
Galvanoscope,  179. 
Gases,  Elasticity  of,  38. 
Gravitation,  15;  Law  of,  16. 


Hardness,  22. 

Harmonics,  273. 

Heat,  121;  Conduction  of,  125; 
Convection  of,  126-129;  Latent, 
143;  Mechanical  equivalent  of, 
151;  of  liquefaction,  142;  Sources 
of,  122;  Specific,  148. 

Hydrometers,  62. 

Hydrostatic  press,  50. 


Images,   Formation   of,   296,   308, 

321. 

Impenetrability,  2. 
Incandescence,  293. 
Induction  coils,  220;  Electrical, 

161;  Electro-magnetic,  216-222; 

Faraday's  law  of,    219;   Lenz's 

law  of,  220. 
Inertia,  70. 
Insulators,  184. 
Isogonic  lines,  208. 


Joule,  184. 

Joule"1  s  equivalent,  150. 


INDEX. 


378 


Kinetic  energy,  100. 

L 

Lenses,  317. 

Lenz's  law  of  induction,  219. 

Light,  Prismatic  analysis  of,  326; 

Undulatory  theory  of,  293.. 
Lightning,  168. 
Light-waves,  Sources  of,  293. 
Liquefaction,  137. 
Locomotive,  156. 
Luminous  objects,  295. 

M 

Machines,  108;  Law  of,  110. 

Magnetic  circuit,  205;  field,  177, 
209;  lines  of  force,  177,  203; 
polarity,  201;  rentivity  and  re- 
sistance, 202;  transparency  and 
induction,  201. 

Magnetism,  Ampere's  theory  of, 
215;  Terrestrial,  206-209. 

Magnets,  Forms  of,  202;  Law  of, 
200. 

Malleability,  25. 

Manometric  flames,  278. 

Mass,  7;  Unit  of,  8. 

Matter,  1,  6;  Amorphous,  22;  Mi- 
nuteness of  particles  of,  6; 
Theory  of  constitution  of,  7; 
Three  states  of,  9. 

Metric  system,  357,  358. 

Microphone,  246. 

Microscope,  Compound,  346; 
Simple,  324. 

Moments  of  forces,  77. 

Momentum,  67. 

Motion,  10;  Graphical  representa- 
tion of,  70;  Newton's  laws  of, 
69,  71,  80. 


N 


Nodes,  251. 


Ohm,  184. 
Ohm's  law,  185. 
Optical  center,  318. 
Overtones,  272. 


Pendulums,  95,  96,  361. 
Penumbra,  298. 
Phenomenon,  1. 
Phonograph,  287. 
Phosphorescence,  293. 
Photometry,  301. 
Physics,  1;  Celestial,  334. 
Pigments,  Mixing,  339. 
Pitch,  Musical,  269. 
Polarization  in  voltaic  cells,  172. 
Porosity,  7. 

Potential,  Electrical,  166,  167. 
Power,  104. 

Pressure,  Atmospheric,  29;  Trans- 
mission of  fluid,  47. 
Prisms,  Optical,  317. 
Pumps  for  liquids,  45,  46. 


Quality  of  sound,  275. 


Radiant  energy,  292. 

Radiation,  129,  342 ;  Only  one  kind 

of,  334. 

Radiators,  345. 
Radiometer,  291. 
Rainbow,  327. 
Ray,  294. 
Reflection,  Law  of,  304 ;  Total,  314. 


374 


INDEX. 


Refraction,  Cause  of,  312;  Double, 

316;  Indices  of,  312. 
Resistance,  Electrical,  184, 188-194. 
Resonators,  264. 
RuhmkorjTs  coil,  222. 


Shadows,  297. 

Shunts,  195. 

Siphon,  54. 

Solenoid,  211. 

Sonometer,  270. 

Sound,  257;  Analysis  of,  275;  In- 
tensity of ,  261;  Quality  of ,  275; 
Synthesis  of,  276. 

Sounding  plates  and  bells,  283. 

Sound-waves,  254-257;  Interference 
of,  266,  285;  Measuring  length 
and  velocity  of,  265 ;  Reenf orce- 
inent  of,  263 ;  Reflection  of,  259 ; 
Speed  of,  258. 

Speaking  tubes,  262. 

Specific  density  and  specific  gravity, 
60;  heat,  148. 

Spectra,  326-334. 

Spectroscope,  330. 

Spectrum  analysis,  333. 

Steam-engine,  152-156. 

Stereopticon,  351. 

Storage  batteries,  234. 


Telegraph,  241-243. 

Telephone,  243-246. 

Telescopes,  348. 

Temperature,   124;  Absolute,  136. 


Tenacity,  20. 

Tension,  26;  Surface,  26. 
Thermo-dynamics,  150. 
Thermo-electric  currents,  235. 
Thermometry,  133. 
Transformer,  232. 
Transparency    and    translucency, 
295. 


Undulatory  theory  of  light,  293. 
Units,  Absolute,  106. 


Vaporization,  137. 

Velocity,  88,  90. 

Ventilation,  128. 

Vibrations,  248-250;   Composition 

of    sonorous,   277;    Forced   and 

sympathetic,  267. 
Viscosity,  24;  Surface,  26. 
Vision,  Defects  of,  350. 
Visual  angle,  303. 
Vocal  organs,  286. 
Volt,  183. 

Voltaic  arc,  237;  cell,  170, 173,  174. 
Volume,  7. 

W 

Watt,  184. 

Wave  motion,  248-254. 
Weight,  8,  16. 
Wheatstone  bridge,  192. 
Wind  instruments,  280. 
Work,     98-100;     Unit    of,     101; 
Wasted,  103. 


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